相关论文: High temperature Sherrington-Kirkpatrick model for…
We calculate the real-time-correlation function of the Sherrington-Kirkpatrick spin-glass model in a transverse field. Using a careful analysis of the perturbative expansion of the functional-integral representation, we derive the…
Based on \cite{H}, it is well known that the rescaled two point correlation functions \[ \sqrt{N} \langle \sigma_i ; \sigma_j\rangle = \sqrt{N} \big( \langle \sigma_i \sigma_j\rangle -\langle \sigma_i\rangle \langle \sigma_j\rangle\big) \]…
In this paper we study the phase diagram of a Sherrington-Kirkpatrick (SK) model where the couplings are forced to thermalize at different time scales. Besides being a challenging generalization of the SK model, such settings may arise…
In this paper, we present a short proof of the limit of free energy of spherical 2 spin Sherrington-Kirkpatrick (SSK) model without external field. This proof works for all temperatures and is based on the Laplace method of integration and…
In a companion paper we developed the generalized TAP approach for general multi-species spherical mixed $p$-spin models. In this paper, we use it to compute the limit of the free energy at any temperature for all pure multi-species…
We investigate the dynamical behavior of the Sherrington-Kirkpatrick mean field model of spin glasses by numerical simulation. All the time scales tau we have measured behave like ln(tau) propto N^epsilon, where N is the number of spins and…
We discuss mean field theory of glasses without quenched disorder focusing on the justification of the replica approach to thermodynamics. We emphasize the assumptions implicit in this method and discuss how they can be verified. The…
Based on the modified Thouless-Anderson-Palmer equations a detailed numerical investigation for the complexity of the Sherrington-Kirkpatrick spin glass is worked out. The data suggest a scaling law which leads to a vanishing of the…
We study the fluctuation problems at high temperature in the general mixed $p$-spin glass models under the weak external field assumption: $h= \rho N^{-\alpha}, \rho>0, \alpha \in [1/4,\infty]$. By extending the cluster expansion approach…
We develop a mean-field theory for random quantum spin systems using the spin coherent state path integral representation. After the model is reduced to the mean field one-body Hamiltonian, the integral is analyzed with the aid of several…
Glass transition where viscosity of liquids increases dramatically upon decrease of temperature without any major change in structural properties, remains one of the most challenging problems in condensed matter physics (Cavagna, 2009;…
Spin relaxation close to the glass temperature of CuMn and AuFe spin glasses is shown, by neutron spin echo, to follow a generalised exponential function which explicitly introduces hierarchically constrained dynamics and macroscopic…
An approximate method is proposed for investigating complex-temperature properties of real-dimensional spin-glass models. The method uses the complex-temperature data of the ferromagnetic model on the same lattice. The universality line in…
We develop further the study of a system in contact with a multibath having different temperatures at widely separated timescales. We consider those systems that do not thermalize in finite times when in contact with an ordinary bath but…
We continue our presentation of mathematically rigorous results about the Sherrington-Kirkpatrick mean field spin glass model. Here we establish some properties of the distribution of overlaps between real replicas. They are in full…
We analyze the Blume-Emery-Griffiths model with disordered magnetic interaction displaying the inverse freezing phenomenon. The behaviour of this spin-1 model in crystal field is studied throughout the phase diagram and the transition and…
Following an original idea of F. Guerra, in this notes we analyze the Sherrington-Kirkpatrick model from different perspectives, all sharing the underlying approach which consists in linking the resolution of the statistical mechanics of…
We introduce a mean field spin glass model with gaussian distribuited spins and pairwise interactions, whose couplings are drawn randomly from a normal gaussian distribution too. We completely control the main thermodynamical properties of…
Inspired by a continuously increasing interest in modeling and framing complex systems in a thermody- namic rationale, in this paper we continue our investigation in adapting well known techniques (originally stemmed in fields of physics…
Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of…