Related papers: Parisi formula for balanced Potts spin glass
We show that the limiting ground state energy of the spherical mixed p-spin model can be identified as the infimum of certain variational problem. This complements the well-known Parisi formula for the limiting free energy in the spherical…
Inspired by the bridge pioneered by Guerra among statistical mechanics on lattice and analytical mechanics on 1+1 continuous Euclidean space-time, we built a self-consistent method to solve for the thermodynamics of mean-field models…
We study a spin system with both mixed even-spin Sherrington-Kirkpatrick (SK) couplings and Curie-Weiss (CW) interaction. Our main results are: (i) The thermodynamic limit of the free energy is given by a variational formula involving the…
In spin-glass systems, frustration can be adjusted continuously and considerably, without changing the antiferromagnetic bond probability p, by using locally correlated quenched randomness, as we demonstrate here on hypercubic lattices and…
The full mean-field solution of spin glass models with a continuous order-parameter function is not directly available and approximate schemes must be used to assess its properties. The averaged physical quantities are to be represented via…
We discuss the response of aging systems with short-range interactions to a class of random perturbations. Although these systems are out of equilibrium, the limit value of the free energy at long times is equal to the equilibrium free…
This work proves an upper bound for the free energy of the Sherrington-Kirkpatrick model and its generalizations in terms of the Thouless-Anderson-Palmer (TAP) energy. The result applies to models with spherical or Ising spins and any mixed…
Expansion for the free energy functionals of the Potts spin glass models with 3, 4 and 5 states up to the fourth order in $\delta q_{\alpha \beta }$ around the replica symmetric solution (RS) is investigated using a special quadrupole-like…
We study the problem of testing and recovering $k$-clique Ferromagnetic mean shift in the planted Sherrington-Kirkpatrick model (i.e., a type of spin glass model) with $n$ spins. The planted SK model -- a stylized mixture of an uncountable…
We prove that the two cornerstones of mean-field spin glass theory -- the Parisi variational formula and the ultrametric organization of pure states -- break down under heavy-tailed disorder. For the mixed spherical $p$-spin model whose…
Considering the unphysical result obtained in the calculation of the free-energy cost for twisting the boundary conditions in a spin glass, we trace it to the negative multiplicities associated with the Parisi replica-symmetry breaking…
The analysis of the solution with full replica symmetry breaking in the vicinity of $T_c$ of a general spin glass model with reflection symmetry is performed. The leading term in the order parameter function expansion is obtained. Parisi…
We investigate overlap fluctuations of the Sherrington-Kirkpatrick mean field spin glass model in the framework of the Random Over- lap Structure (ROSt). The concept of ROSt has been introduced recently by Aizenman and coworkers, who…
A generalization of the Sherrington-Kirkpatrick (SK) model for spin glasses is considered, in which the interaction matrix is endowed with a variance profile that has no particular structure an may be sparse. In the first part of this…
We consider the problem of algorithmically sampling from the Gibbs measure of a mixed $p$-spin spherical spin glass. We give a polynomial-time algorithm that samples from the Gibbs measure up to vanishing total variation error, for any…
We study the L\'evy spin glass model, a fully connected model on $N$ vertices with heavy-tailed interactions governed by a power law distribution of order $0<\alpha<2.$ Our investigation is divided into three cases $0<\alpha<1$, $\alpha=1$,…
We introduce a new disordered system, the Super-Potts model, which is a more frustrated version of the Potts glass. Its elementary degrees of freedom are variables that can take M values and are coupled via pair-wise interactions. Its exact…
In this note, we consider the multi-species Sherrington-Kirkpatrick spin glass model at its conjectured critical temperature, and we show that, when the variance profile matrix $\Delta^2$ is positive semi-definite, the variance of the free…
The free energy of any system can be written as the supremum of a functional involving an energy term and an entropy term. Surprisingly, the limit free energy of mean-field spin glasses is expressed as an infimum instead, a phenomenon…
We study a three-dimensional plaquette spin model whose low temperature dynamics is glassy, due to localised defects and effective kinetic constraints. While the thermodynamics of this system is smooth at all temperatures, we show that…