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Related papers: The cavity method at zero temperature

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The spin-glass transition in a field in finite dimension is analyzed directly at zero temperature using a perturbative loop expansion around the Bethe lattice solution. The loop expansion is generated by the $M$-layer construction whose…

Disordered Systems and Neural Networks · Physics 2022-03-18 Maria Chiara Angelini , Carlo Lucibello , Giorgio Parisi , Gianmarco Perrupato , Federico Ricci-Tersenghi , Tommaso Rizzo

In an extremely influential paper Mezard and Parisi put forward an analytic but non-rigorous approach called the cavity method for studying spin systems on the Bethe lattice, i.e., the random $d$-regular graph [Eur. Phys. J. B 20 (2001)…

Probability · Mathematics 2019-09-04 Amin Coja-Oghlan , Will Perkins

A theory for the complexity of the Bethe lattice spin-glass is developed applying to the cavity-method scheme of Mezard and Parisi the results recently obtained in the context of the Sherrington-Kirkpatrick model. The crucial ingredient is…

Disordered Systems and Neural Networks · Physics 2007-05-23 Tommaso Rizzo

A model of spinless interacting electrons in presence of randomness is examined using an extended dynamical mean-field formulation. When the interaction strength is large as compared to the Fermi energy, a low temperature glassy phase is…

Disordered Systems and Neural Networks · Physics 2009-10-31 A. A. Pastor , V. Dobrosavljevic

A wide class of problems in combinatorics, computer science and physics can be described along the following lines. There are a large number of variables ranging over a finite domain that interact through constraints that each bind a few…

Probability · Mathematics 2017-11-17 Victor Bapst , Amin Coja-Oghlan

We study the phase diagram at finite temperature of a system of Fermi particles on the sites of the Bethe lattice with coordination number z and interacting through onsite U and nearest-neighbor V interactions. This is a physical…

Strongly Correlated Electrons · Physics 2008-09-09 F. Mancini , F. P. Mancini , A. Naddeo

We present a numerical method to generate explicit realizations of the tree of states in mean-field spin glasses. The resulting study illuminates the physical meaning of the full replica symmetry breaking solution and provides detailed…

Disordered Systems and Neural Networks · Physics 2015-05-08 G. Parisi , F. Ricci-Tersenghi , D. Yllanes

The mixed spin-1/2 and spin-5/2 Ising model is investigated on the Bethe lattice in the presence of a magnetic field $h$ via the recursion relations method. A ground-state phase diagram is constructed which may be needful to explore…

Statistical Mechanics · Physics 2017-02-13 M. Karimou , R. A. Yessoufou , T. D. Oke , A. Kpadonou , F. Hontinfinde

We propose a two-step procedure to study the order of phase transitions at finite temperature in electroweak theory and in simplified models thereof. In a first step a coarse grained free energy is computed by perturbative methods. It is…

High Energy Physics - Lattice · Physics 2009-10-28 U. Kerres , G. Mack , G. Palma

Zeros of the moment of the partition function $[Z^n]_{\bm{J}}$ with respect to complex $n$ are investigated in the zero temperature limit $\beta \to \infty$, $n\to 0$ keeping $y=\beta n \approx O(1)$. We numerically investigate the zeros of…

Disordered Systems and Neural Networks · Physics 2015-05-18 Tomoyuki Obuchi , Yoshiyuki Kabashima , Hidetoshi Nishimori , Masayuki Ohzeki

We compute the critical exponents of the zero-temperature spin glass transition in a field on a one-dimensional long-range model, a proxy for higher-dimensional systems. Our approach is based on a novel loop expansion within the Bethe…

Disordered Systems and Neural Networks · Physics 2026-02-23 Maria Chiara Angelini , Saverio Palazzi , Giorgio Parisi , Tommaso Rizzo

The average ground state energies for spin glasses on Bethe lattices of connectivities r=3,...,15 are studied numerically for a Gaussian bond distribution. The Extremal Optimization heuristic is employed which provides high-quality…

Disordered Systems and Neural Networks · Physics 2010-04-13 S. Boettcher

A new approach known as flat histogram method is used to study the +/-J Ising spin glass in two dimensions. Temperature dependence of the energy, the entropy, and other physical quantities can be easily calculated and we give the results…

Statistical Mechanics · Physics 2009-10-31 Zhi Fang Zhan , Lik Wee Lee , Jian-Sheng Wang

Bethe lattice spins glasses are supposed to be marginally stable, i.e. their equilibrium probability distribution changes discontinuously when we add an external perturbation. So far the problem of a spin glass on a Bethe lattice has been…

Disordered Systems and Neural Networks · Physics 2017-05-24 Giorgio Parisi

We propose a definition of vorticity at inverse temperature \beta for Gibbs states in quantum XY spin systems on the lattice by testing \exp[-\beta H] on a complete set of observables ("one-point functions"). We show in particular that it…

Mathematical Physics · Physics 2015-04-07 Dimitri Minenkov , Michel Rouleux

In this note I present a simplified version of the recent computation (Mezard and Parisi 1998, 1999) of the properties of glasses in the low temperature phase in the framework of the replica theory, using an extension of the tools used in…

Soft Condensed Matter · Physics 2017-02-08 Giorgio Parisi

We construct a mean field theory for the lattice model of a structural glass and solve it using the replica method and one step replica symmetry breaking ansatz; this theory becomes exact in the limit of infinite dimensions. Analyzing…

Disordered Systems and Neural Networks · Physics 2009-11-07 A. V. Lopatin , L. B. Ioffe

In the present paper the three state Potts model with competing binary interactions (with couplings $J$ and $J_p$) on the second order Bethe lattice is considered. The recurrent equations for the partition functions are derived. When…

Mathematical Physics · Physics 2009-11-11 Nasir Ganikhodjaev , Farrukh Mukhamedov , Jose F. F. Mendes

At sufficiently low temperatures, the configurational phase space of a large spin-glass system breaks into many separated domains, each of which is referred to as a macroscopic state. The system is able to visit all spin configurations of…

Disordered Systems and Neural Networks · Physics 2009-11-13 Haijun Zhou

We study zero temperature properties of a system of two coupled quantum spin chains subject to fields explicitly breaking time reversal symmetry and parity. Suitable choice of the strength of these fields gives a model soluble by Bethe…

Statistical Mechanics · Physics 2009-10-30 Holger Frahm , Claus Rödenbeck