Publications – Statistical Physics of Disordered Systems (SPoDS)

A complete list of publications. Books and book chapters are listed first, followed by preprints and by articles in peer-reviewed international journals in reverse chronological order.

Books

L. Leuzzi, E. Marinari, G. Parisi, Probability Theory for Quantitative Scientists, Cambridge University Press (2025). ISBN 9781009580656.
L. Leuzzi, E. Marinari, G. Parisi, Calcolo delle probabilità. Un trattatello per principianti volenterosi, Zanichelli (2023). ISBN 9788808499660.
L. Leuzzi, T. M. Nieuwenhuizen, Thermodynamics of the Glassy State, CRC Press – Taylor & Francis (2008). ISBN 9780750309974.

Book chapters

C. Conti, N. Ghofraniha, L. Leuzzi, G. Ruocco, Replica Symmetry Breaking in Random Lasers: Experimental Measurement of the Overlap Distribution, in Spin Glass Theory and Far Beyond, World Scientific (2023), pp. 307–334. doi:10.1142/9789811273926_0016
I. Viola, L. Leuzzi, C. Conti, N. Ghofraniha, Basic Physics and Recent Developments of Organic Random Lasers, in Organic Lasers: Fundamentals, Developments, and Applications (2018), pp. 151–192.
A. Crisanti, L. Leuzzi, Large Deviations in Disordered Spin Systems, in Large Deviations in Physics, Lecture Notes in Physics 885, Springer (2014), pp. 135–160.

Preprints

T. De Chirico, L. Leuzzi, Quenched complexity of marginal states in the Sherrington–Kirkpatrick spin glass (2026). arXiv:2609.04006
J. Lang, V. Citro, L. Leuzzi, F. Ricci-Tersenghi, Aging phase diagram and exact asymptotic energies of mixed spherical spin glasses (2026). arXiv:2608.20623
T. Giordani, G. Zanfardino, L. Leuzzi, E. Bonfissuto, E. Caruccio, G. Gasbarri, M. Bossi, A. Rajan, R. Albiero, F. Ceccarelli, N. Spagnolo, R. Santagati, S. Paesani, M. Leonetti, R. Osellame, G. Parisi, G. Ruocco, F. Illuminati, F. Sciarrino, Observation of associative-memory retrieval and spin-glass phases on a photonic quantum simulator (2026). arXiv:2605.22922
J. Lang, V. Citro, L. Leuzzi, F. Ricci-Tersenghi, DYNAMITE: A high-performance framework for solving Dynamical Mean-Field Equations (2026). arXiv:2604.06309
S. Bae, D. Bocchi, L. M. Del Bono, L. Leuzzi, Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition (2025). arXiv:2507.02574

Articles in peer-reviewed international journals

2026

M. Benedetti, L. Leuzzi, Smoothed-Cubic Spin-Glass Model of Random Lasers, SciPost Phys. 20, 153 (2026). doi:10.21468/SciPostPhys.20.6.153
A. L. Muthali, P. I. Sund, C. F. D. Faurby, Ç. Ekici, J. C. Adcock, J. Glindemann, G. Zanfardino, L. Leuzzi, R. Santagati, F. Illuminati, G. Ruocco, M. Leonetti, S. Paesani, Y. Ding, Adv. Photonics Nexus 5, 025001 (2026). doi:10.1117/1.APN.5.2.025001
G. Zanfardino, S. Paesani, L. Leuzzi, R. Santagati, F. Illuminati, G. Ruocco, M. Leonetti, Multiphoton quantum simulation of the generalized Hopfield memory model, Phys. Rev. Lett. 136, 070602 (2026).

2024

L. Leuzzi, T. Rizzo, Logarithmic critical slowing down in complex systems: From statics to dynamics, Phys. Rev. B 109, 174211 (2024). doi:10.1103/PhysRevB.109.174211
D. Ancora, M. Negri, A. Gianfrate, D. Trypogeorgos, L. Dominici, D. Sanvitto, F. Ricci-Tersenghi, L. Leuzzi, Low-power multimode-fiber projector outperforms shallow-neural-network classifiers, Phys. Rev. Applied 21, 064027 (2024). doi:10.1103/PhysRevApplied.21.064027

2023

M. Leonetti, L. Leuzzi, G. Ruocco, Reference-less wavefront shaping in a Hopfield-like rough intensity landscape, Opt. Express 31, 28987 (2023). doi:10.1364/OE.492055
J. Niedda, G. Gradenigo, L. Leuzzi, G. Parisi, Universality class of the mode-locked glassy random laser, SciPost Phys. 14, 144 (2023). doi:10.21468/SciPostPhys.14.6.144
J. Niedda, L. Leuzzi, G. Gradenigo, Intensity pseudo-localized phase in the glassy random laser, J. Stat. Mech. 053302 (2023). doi:10.1088/1742-5468/acd2c4
N. Lauber, O. Tichacek, R. Bose, C. Flamm, L. Leuzzi, T.-Y. D. Tang, K. Ruiz-Mirazo, D. De Martino, Statistical mechanics of biomolecular condensates via cavity methods, iScience 26, 106300 (2023). doi:10.1016/j.isci.2023.106300

2022

L. Leuzzi, A. Patti, F. Ricci-Tersenghi, A quantitative analysis of a generalized Hopfield model that stores and retrieves mismatched memory patterns, J. Stat. Mech. (2022). doi:10.1088/1742-5468/ac7e40
D. Ancora, L. Dominici, A. Gianfrate, P. Cazzato, M. De Giorgi, D. Ballarini, D. Sanvitto, L. Leuzzi, Speckle spatial correlations aiding optical transmission matrix retrieval, Photonics Res. 10, 2349 (2022). doi:10.1364/PRJ.462578
D. Ancora, L. Leuzzi, Transmission matrix inference via pseudolikelihood decimation, J. Phys. A 55 (2022). doi:10.1088/1751-8121/ac8c06
M. G. Izzo, C. Daraio, L. Leuzzi, G. Quaglia, G. Ruocco, Worldwide bilateral geopolitical interactions network inferred from national disciplinary profiles, Phys. Rev. Research 4, 023224 (2022). doi:10.1103/PhysRevResearch.4.023224

2021

F. Antenucci, G. Lerario, B. S. Fernandez, L. De Marco, M. De Giorgi, D. Ballarini, D. Sanvitto, L. Leuzzi, Demonstration of Self-Starting Nonlinear Mode Locking in Random Lasers, Phys. Rev. Lett. 126, 173901 (2021). doi:10.1103/PhysRevLett.126.173901
M. Leonetti, E. Hormann, L. Leuzzi, G. Parisi, G. Ruocco, Optical computation of a spin glass dynamics with tunable complexity, PNAS 118 (2021). doi:10.1073/pnas.2015207118

2020

G. Gradenigo, F. Antenucci, L. Leuzzi, Glassiness and lack of equipartition in random lasers, Phys. Rev. Research 2, 023399 (2020). doi:10.1103/PhysRevResearch.2.023399
M. B. Bostian, C. Daraio, R. Fare, S. Grosskopf, M. G. Izzo, L. Leuzzi, G. Ruocco, W. L. Weber, Reconstructing Nonparametric Productivity Networks, Entropy 22, 1401 (2020). doi:10.3390/e22121401
G. Gradenigo, M. C. Angelini, L. Leuzzi, F. Ricci-Tersenghi, Solving the spherical p-spin model with the cavity method, J. Stat. Mech. (2020). doi:10.1088/1742-5468/abc4e3
M. Dilucca, L. Leuzzi, G. Parisi, F. Ricci-Tersenghi, J. J. Ruiz-Lorenzo, Spin Glasses in a Field Show a Phase Transition Varying the Distance among Real Replicas, Entropy 22, 250 (2020). doi:10.3390/e22020250

2018

C. Daraio, F. Fabbri, G. Gavazzi, M. G. Izzo, L. Leuzzi, G. Quaglia, G. Ruocco, Assessing the interdependencies between scientific disciplinary profiles, Scientometrics 116, 1785 (2018). doi:10.1007/s11192-018-2816-5
A. Marruzzo, P. Tyagi, F. Antenucci, A. Pagnani, L. Leuzzi, Improved pseudolikelihood regularization and decimation methods on non-linearly interacting systems with continuous variables, SciPost Phys. 5 (2018). doi:10.21468/SciPostPhys.5.1.002

2017

A. Marruzzo, P. Tyagi, F. Antenucci, A. Pagnani, L. Leuzzi, Inverse problem for multi-body interaction of nonlinear waves, Sci. Rep. 7 (2017). doi:10.1038/s41598-017-03163-4
S. Colabrese, D. De Martino, L. Leuzzi, E. Marinari, Phase transitions in integer linear problems, J. Stat. Mech. (2017). doi:10.1088/1742-5468/aa85c3

2016

A. Marruzzo, L. Leuzzi, Multi-body quenched disordered XY and p-clock models on random graphs, Phys. Rev. B 93, 094206 (2016). doi:10.1103/PhysRevB.93.094206
P. Tyagi, A. Marruzzo, A. Pagnani, F. Antenucci, L. Leuzzi, Regularization and decimation pseudolikelihood approaches to statistical inference in XY spin models, Phys. Rev. B 94, 024203 (2016). doi:10.1103/PhysRevB.94.024203
F. Antenucci, A. Crisanti, M. Ibanez-Berganza, A. Marruzzo, L. Leuzzi, Statistical mechanics models for multimode lasers and random lasers, Philos. Mag. 96, 704 (2016). doi:10.1080/14786435.2016.1145359

2015

A. Crisanti, L. Leuzzi, A simple spin model for three step relaxation and secondary processes in glass formers, J. Non-Cryst. Solids 407, 110 (2015). doi:10.1016/j.jnoncrysol.2014.07.048
F. Antenucci, A. Crisanti, L. Leuzzi, Complex spherical 2+4 spin glass: A model for nonlinear optics in random media, Phys. Rev. A 91, 053816 (2015). doi:10.1103/PhysRevA.91.053816
C. Rainone, U. Ferrari, M. Paoluzzi, L. Leuzzi, Dynamical arrest with zero complexity: the unusual behavior of the spherical Blume–Emery–Griffiths disordered model, Phys. Rev. E 92, 062150 (2015). doi:10.1103/PhysRevE.92.062150
N. Ghofraniha, I. Viola, F. Di Maria, G. Barbarella, G. Gigli, L. Leuzzi, C. Conti, Experimental evidence of replica symmetry breaking in random lasers, Nat. Commun. 6, 7058 (2015). doi:10.1038/ncomms7058
F. Antenucci, C. Conti, A. Crisanti, L. Leuzzi, General Phase Diagram of Multimodal Ordered and Disordered Lasers in Closed and Open Cavities, Phys. Rev. Lett. 114, 043901 (2015). doi:10.1103/PhysRevLett.114.043901
P. Tyagi, A. Pagnani, F. Antenucci, M. Ibanez Berganza, L. Leuzzi, Inference for interacting linear waves in ordered and random media, J. Stat. Mech. P05031 (2015). doi:10.1088/1742-5468/2015/05/P05031
L. Leuzzi, G. Parisi, F. Ricci-Tersenghi, J. J. Ruiz-Lorenzo, Infinite volume extrapolation in the one-dimensional bond diluted Lévy spin-glass model near its lower critical dimension, Phys. Rev. B 91, 064202 (2015). doi:10.1103/PhysRevB.91.064202
A. Marruzzo, L. Leuzzi, Nonlinear XY and p-clock models on sparse random graphs: mode-locking transition of localized waves, Phys. Rev. B 91, 054201 (2015). doi:10.1103/PhysRevB.91.054201
F. Antenucci, M. Ibanez Berganza, L. Leuzzi, Statistical physical theory of mode-locking laser generation with a frequency comb, Phys. Rev. A 91, 043811 (2015). doi:10.1103/PhysRevA.91.043811
F. Antenucci, M. Ibanez Berganza, L. Leuzzi, Statistical physics of nonlinear wave interaction, Phys. Rev. B 92, 014204 (2015). doi:10.1103/PhysRevB.92.014204
F. Antenucci, A. Crisanti, L. Leuzzi, The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra, Sci. Rep. 5, 16792 (2015). doi:10.1038/srep16792

2014

F. Antenucci, A. Crisanti, L. Leuzzi, Critical Study of Hierarchical Lattice Renormalization Group in Magnetic Ordered and Quenched Disordered Systems, J. Stat. Phys. 155, 909 (2014). doi:10.1007/s10955-014-0977-z
F. L. Metz, G. Parisi, L. Leuzzi, Finite-size corrections to the spectrum of regular random graphs: an analytical solution, Phys. Rev. E 90, 052109 (2014). doi:10.1103/PhysRevE.90.052109
F. L. Metz, L. Leuzzi, G. Parisi, Renormalization flow of the hierarchical Anderson model at weak disorder, Phys. Rev. B 89, 064201 (2014). doi:10.1103/PhysRevB.89.064201
F. Antenucci, A. Crisanti, L. Leuzzi, Small-cluster renormalization group in Ising and Blume–Emery–Griffiths models, Phys. Rev. E 90, 012112 (2014). doi:10.1103/PhysRevE.90.012112

2013

M. Ibanez Berganza, L. Leuzzi, Critical behavior of the XY model in complex topologies, Phys. Rev. B 88, 144104 (2013). doi:10.1103/PhysRevB.88.144104
A. Crisanti, L. Leuzzi, Exactly solvable spin-glass models with ferromagnetic couplings: the spherical multi-p-spin model in a self-induced field, Nucl. Phys. B 870, 176 (2013). doi:10.1016/j.nuclphysb.2013.01.011
L. Leuzzi, G. Parisi, Long-range random-field Ising model: phase transition threshold and equivalence of short and long ranges, Phys. Rev. B 88, 224204 (2013). doi:10.1103/PhysRevB.88.224204
V. Folli, N. Ghofraniha, A. Puglisi, L. Leuzzi, C. Conti, Time-resolved dynamics of granular matter by random laser emission, Sci. Rep. 3, 2251 (2013). doi:10.1038/srep02251
F. L. Metz, L. Leuzzi, G. Parisi, V. Sacksteder, Transition between localized and extended states in the hierarchical Anderson model, Phys. Rev. B 88, 045103 (2013). doi:10.1103/PhysRevB.88.045103

2012

Y. Sun, A. Crisanti, F. Krzakala, L. Leuzzi, L. Zdeborová, Following states in temperature in the spherical s+p-spin glass model, J. Stat. Mech. P07002 (2012). doi:10.1088/1742-5468/2012/07/P07002
F. Caltagirone, U. Ferrari, L. Leuzzi, G. Parisi, T. Rizzo, Critical slowing down exponents in structural glasses: random orthogonal and related models, Phys. Rev. B 86, 064204 (2012). doi:10.1103/PhysRevB.86.064204
F. Caltagirone, U. Ferrari, L. Leuzzi, G. Parisi, F. Ricci-Tersenghi, T. Rizzo, Critical slowing down exponents of mode coupling theory, Phys. Rev. Lett. 108, 085702 (2012). doi:10.1103/PhysRevLett.108.085702
V. Folli, A. Puglisi, L. Leuzzi, C. Conti, Shaken Granular Lasers, Phys. Rev. Lett. 108, 248002 (2012). doi:10.1103/PhysRevLett.108.248002
U. Ferrari, L. Leuzzi, G. Parisi, T. Rizzo, Two-step relaxation next to dynamic arrest in mean-field glasses, Phys. Rev. B 86, 014204 (2012). doi:10.1103/PhysRevB.86.014204

2011

L. Leuzzi, G. Parisi, F. Ricci-Tersenghi, J. J. Ruiz-Lorenzo, Bond diluted Lévy spin-glass model and a new finite-size scaling method to determine a phase transition, Philos. Mag. 91, 1917 (2011). doi:10.1080/14786435.2010.534741
C. Conti, L. Leuzzi, Complexity of waves in nonlinear disordered media, Phys. Rev. B 83, 134204 (2011). doi:10.1103/PhysRevB.83.134204
F. Caltagirone, U. Ferrari, L. Leuzzi, G. Parisi, T. Rizzo, Ising M-p-spin mean-field model for the structural glass: continuous versus discontinuous transition, Phys. Rev. B 83, 104202 (2011). doi:10.1103/PhysRevB.83.104202
L. Leuzzi, M. Paoluzzi, A. Crisanti, Random Blume–Capel model on a cubic lattice: first-order inverse freezing in a three-dimensional spin-glass system, Phys. Rev. B 83, 014107 (2011). doi:10.1103/PhysRevB.83.014107
U. Ferrari, L. Leuzzi, Random, thermodynamic and inverse first-order transitions in the Blume–Capel spin glass, J. Stat. Mech. P12005 (2011). doi:10.1088/1742-5468/2011/12/P12005
A. Crisanti, L. Leuzzi, M. Paoluzzi, Statistical mechanical approach to secondary processes and structural relaxation in glasses and glass formers, Eur. Phys. J. E 34 (2011). doi:10.1140/epje/i2011-11098-3
M. Paoluzzi, L. Leuzzi, A. Crisanti, The overlap parameter across an inverse first-order phase transition in a 3D spin-glass, Philos. Mag. 91, 1966 (2011). doi:10.1080/14786435.2010.535257

2010

M. Paoluzzi, L. Leuzzi, A. Crisanti, Thermodynamic First Order Transition and Inverse Freezing in a 3D Spin Glass, Phys. Rev. Lett. 104, 120602 (2010). doi:10.1103/PhysRevLett.104.120602

2009

L. Leuzzi, A stroll among effective temperatures in aging systems: limits and perspectives, J. Non-Cryst. Solids 355, 686 (2009). doi:10.1016/j.jnoncrysol.2009.01.035
L. Leuzzi, G. Parisi, F. Ricci-Tersenghi, J. J. Ruiz-Lorenzo, Ising Spin-Glass Transition in a Magnetic Field Outside the Limit of Validity of Mean-Field Theory, Phys. Rev. Lett. 103, 267201 (2009). doi:10.1103/PhysRevLett.103.267201
L. Leuzzi, C. Conti, V. Folli, L. Angelani, G. Ruocco, Phase diagram and complexity of mode-locked lasers: from order to disorder, Phys. Rev. Lett. 102 (2009).

1999 – 2008

L. Leuzzi, G. Parisi, F. Ricci-Tersenghi, J. J. Ruiz-Lorenzo, Dilute one-dimensional spin glasses with power law decaying interactions, Phys. Rev. Lett. 101 (2008).
L. Leuzzi, Static and dynamic glass-glass transitions: a mean-field study, Philos. Mag. 88, 4015 (2008).
A. Crisanti, L. Leuzzi, Amorphous-amorphous transition and the two-step replica symmetry breaking phase, Phys. Rev. B 76 (2007).
A. Crisanti, L. Leuzzi, Equilibrium dynamics of spin-glass systems, Phys. Rev. B 75 (2007).
A. Crisanti, L. Leuzzi, Reply to “Comment on: Spherical 2+p spin-glass model”, Phys. Rev. B 76 (2007).
L. Leuzzi, Spin-glass model for inverse freezing, Philos. Mag. 87, 543 (2007).
G. Aquino, L. Leuzzi, T. M. Nieuwenhuizen, Kovacs effect in a model for a fragile glass, Phys. Rev. B 73 (2006).
M. Müller, L. Leuzzi, A. Crisanti, Marginal states in mean-field glasses, Phys. Rev. B 74 (2006).
L. Leuzzi, A. Crisanti, Spherical 2+p spin-glass model: an analytically solvable model with a glass-to-glass transition, Phys. Rev. B 73 (2006).
G. Aquino, L. Leuzzi, T. M. Nieuwenhuizen, Kovacs effect in solvable model glasses, J. Phys. Conf. Ser. 40, 50 (2006).
A. Crisanti, L. Leuzzi, T. Rizzo, Complexity in mean-field spin-glass models: Ising p-spin, Phys. Rev. B 71, 094202 (2005). doi:10.1103/PhysRevB.71.094202
L. Leuzzi, Complexity in mean-field spin-glasses, Prog. Theor. Phys. Suppl. 157, 94 (2005).
A. Crisanti, L. Leuzzi, Stable solution of the simplest spin model for inverse freezing, Phys. Rev. Lett. 95 (2005).
A. Crisanti, L. Leuzzi, G. Parisi, T. Rizzo, Quenched computation of the dependence of complexity on the free energy in the Sherrington–Kirkpatrick model, Phys. Rev. B 70 (2004).
A. Crisanti, L. Leuzzi, Spherical 2+p spin-glass model: an exactly solvable model for glass to spin-glass transition, Phys. Rev. Lett. 93 (2004).
A. Crisanti, L. Leuzzi, G. Parisi, T. Rizzo, Spin-glass complexity, Phys. Rev. Lett. 92 (2004).
A. Crisanti, L. Leuzzi, Thermodynamic properties of a full-replica-symmetry-breaking Ising spin glass on lattice gas: the random Blume–Emery–Griffiths–Capel model, Phys. Rev. B 70 (2004).
A. Crisanti, L. Leuzzi, G. Parisi, T. Rizzo, Complexity in the Sherrington–Kirkpatrick model in the annealed approximation, Phys. Rev. B 68 (2003).
A. Crisanti, L. Leuzzi, T. Rizzo, The complexity of the spherical p-spin spin glass model, revisited, Eur. Phys. J. B 36, 129 (2003).
L. Leuzzi, F. Ritort, Disordered backgammon model, Phys. Rev. E 65 (2002).
L. Leuzzi, T. M. Nieuwenhuizen, Exactly solvable model glass with facilitated dynamics, J. Phys.: Condens. Matter 14, 1637 (2002).
A. Crisanti, L. Leuzzi, First-order phase transition and phase coexistence in a spin-glass model, Phys. Rev. Lett. 89 (2002).
A. Crisanti, L. Leuzzi, G. Parisi, The 3-SAT problem with large number of clauses in the ∞-replica symmetry breaking scheme, J. Phys. A 35, 481 (2002).
L. Leuzzi, T. M. Nieuwenhuizen, Effective temperatures in an exactly solvable model for a fragile glass, Phys. Rev. E 64 (2001).
L. Leuzzi, T. M. Nieuwenhuizen, Inherent structures in models for fragile and strong glass, Phys. Rev. E 64 (2001).
L. Leuzzi, G. Parisi, The K-SAT problem in a simple limit, J. Stat. Phys. 103, 679 (2001).
L. Leuzzi, G. Parisi, Thermodynamics of a tiling model, J. Phys. A 33, 4215 (2000).
L. Leuzzi, Critical behaviour and ultrametricity of Ising spin-glass with long-range interactions, J. Phys. A 32, 1417 (1999).

Other publications

A. Cavagna, S. Franz, I. Giardina, L. Leuzzi, A. Maiorano, E. Marinari, F. Ricci-Tersenghi, T. Rizzo, F. Zamponi, Preface to the special issue on “Disordered serendipity: a glassy path to discovery”, J. Phys. A 53 (2020). doi:10.1088/1751-8121/abbd55
L. Leuzzi, Foreword, in F. Antenucci, Statistical Physics of Wave Interactions, Springer (2016), pp. V–VII.
L. Leuzzi, E. Marinari, G. Parisi, F. Ricci-Tersenghi, La letalità apparente e quella reale di COVID-19, Le Scienze, 13 May 2020.
E. Bucci, L. Leuzzi, E. Marinari, G. Parisi, F. Ricci-Tersenghi, Verso una stima di morti dirette e indirette per Covid, Scienza in Rete, 24 April 2020.