相关论文: The SK model with a sparse variance profile: free …
We solve the $S=1/2$ infinite-range random Heisenberg Hamiltonian in the paramagnetic phase using quantum Monte Carlo and analytical techniques. We find that the spin-glass susceptibility diverges at a finite temperature $T_g$ which…
We introduce a variational algorithm based on Matrix Product States that is trained by minimizing a generalized free energy defined using Tsallis entropy instead of the standard Gibbs entropy. As a result, our model can generate the…
We consider vector spin glasses whose energy function is a Gaussian random field with covariance given in terms of the matrix of scalar products. For essentially any model in this class, we give an upper bound for the limit free energy,…
We investigate scenarios in which the low-temperature phase of short-range spin glasses comprises thermodynamic states which are nontrivial mixtures of multiple incongruent pure state pairs. We construct a new kind of metastate supported on…
20 years ago, Bovier, Kurkova, and L\"owe [5] proved a central limit theorem (CLT) for the fluctuations of the free energy in the p-spin version of the Sherrington-Kirkpatrick model of spin glasses at high temperatures. In this paper we…
We consider the free energy of a mean-field quantum spin glass described by a $ p $-spin interaction and a transversal magnetic field. Recent rigorous results for the case $ p= \infty $, i.e. the quantum random energy model (QREM), are…
The dynamic linear response theory of a general Ising model weakly coupled to a heat bath is derived employing the quantum statistical theory of Mori, treating the Hamiltonian of the spin bath coupling as a perturbation, and applying the…
We introduce efficient algorithms for approximate sampling from symmetric Gibbs distributions on the sparse random (hyper)graph. The examples we consider include (but are not restricted to) important distributions on spin systems and…
We explore a one-to-one correspondence between a neural network (NN) and a statistical mechanical spin model where neurons are mapped to Ising spins and weights to spin-spin couplings. The process of training an NN produces a family of spin…
In many spin glass models, due to the symmetry among sites, any limiting joint distribution of spins under the annealed Gibbs measure admits the Aldous-Hoover representation encoded by a function $\sigma:[0,1]^4\to\{-1,+1\}$, and one can…
Results regarding spin glass models are, to this day, mainly confined to models with Ising spins. Spin glass models with continuous spins exhibit interesting new physical behaviors related to the additional degrees of freedom, but have been…
In the Sherrington-Kirkpatrick mean field model for spin glasses, we show that the quenched average of the free energy can be expressed through a couple of functional order parameters, in a form very similar to the one found in the frame of…
The study of the mean-field static solution of the Random Blume-Emery-Griffiths-Capel model, an Ising-spin lattice gas with quenched random magnetic interaction, is performed. The model exhibits a paramagnetic phase, described by a stable…
We study the problem of chaos in temperature in some mean-field spin-glass models by means of a replica computation over a model of coupled systems. We propose a set of solutions of the saddle point equations which are intrinsically…
We give an asymptotic evaluation of the complexity of spherical p-spin spin-glass models via random matrix theory. This study enables us to obtain detailed information about the bottom of the energy landscape, including the absolute minimum…
We consider the Ising spin glass for the arbitrary spin S with the short- ranged interaction using the Bethe- Peierls approximation previously formulated by Serva and Paladin for the same system but limited to S=1/2. Results obtained by us…
We show that any SYK-like model with finite-body interactions among \textit{local} degrees of freedom, e.g., bosons or spins, has a fundamental difference from the standard fermionic model: the former fails to be described by an annealed…
The Complexity of the Thouless-Anderson-Palmer (TAP) solutions of the Ising $p$-spin is investigated in the temperature regime where the equilibrium phase is one step Replica Symmetry Breaking. Two solutions of the resulting saddle point…
A spin-wave theory of short-range order in the square lattice Heisenberg antiferromagnet is formulated. With growing temperature from T=0 a gapless mode is shown to arise simultaneously with opening a gap in the conventional spin-wave mode.…
We have simulated Edwards-Anderson (EA) as well as Sherrington-Kirkpatrick systems of L^3 spins. After averaging over large sets of EA system samples of 3 =< L =< 10, we obtain accurate numbers for distributions p(q) of the overlap…