Related papers: The Complexity of Ising Spin Glasses
This key-issues review is a plea for a new focus on simpler and more realistic models of glass-forming fluids. It seems to me that we have too often been led astray by sophisticated mathematical models that beautifully capture some of the…
For the dynamical glassy transition in the $p$-spin mean field spin glass model a thermodynamic description is given. The often considered marginal states are not the relevant ones for this purpose. This leads to consider a cooling…
We present a unified exact tensor network approach to compute the ground state energy, identify the optimal configuration, and count the number of solutions for spin glasses. The method is based on tensor networks with the Tropical Algebra…
We show that mixing for local, reversible dynamics of mean field spin glasses is exponentially slow in the low temperature regime. We introduce a notion of free energy barriers for the overlap, and prove that their existence imply that the…
There is a new class of two-dimensional magnetic materials polymeric iron (III) acetate fabricated recently in which Fe ions form a star lattice. We study the thermodynamics of Ising spins on the star lattice with exact analytic method and…
In spin glass models one can remove minimization of free energy by some order parameter. One can consider hierarchy of order parameters. It is possible to divide energy among these parts. We can consider relaxation process in glass system…
Small spin systems at the interface between analytical studies and experimental application have been intensively studied in recent decades. The spin ring consisting of four spins with uniform antiferromagnetic Heisenberg interaction is an…
Aim of this work is not trying to explore a macroscopic behavior of some recent model in statistical mechanics but showing how some recent techniques developed within the framework of spin glasses do work on simpler model, focusing on the…
Spin glasses are disordered magnetic systems that exhibit a variety of properties that are characteristic of complex systems. After a brief review of basic spin glass concepts, their use in areas such as computer science, biology, and other…
We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two…
This paper characterizes the annealed complexity of bipartite spherical spin glasses, both pure and mixed. This means we give exact variational formulas for the asymptotics of the expected numbers of critical points and of local minima.…
We propose an iterative algorithm for solving the Thouless-Anderson-Palmer (TAP) equations of Ising models with arbitrary rotation invariant (random) coupling matrices. In the thermodynamic limit, we prove by means of the dynamical…
It is shown that continuously changing the effective number of interacting particles in p-spin-glass-like model allows to describe the transition from the full replica symmetry breaking glass solution to stable first replica symmetry…
The spin degree of freedom can play an essential role in determining the electrical transport properties of spin-polarized electron systems in metals or semiconductors. In this article, I address the dependence of spin-subsystem chemical…
In these lectures I will present an introduction to the modern way of studying the properties of glassy systems. I will start from soluble models of increasing complications, the Random Energy Model, the $p$-spins interacting model and I…
Relaxation phenomena in glasses can be related to jump processes between different minima of the potential energy in the configuration space. These transitions play a key role in the low temperature regime, giving rise to tunneling systems…
The relationship between the spectral density and free energy of a spin system is considered. The analytical expressions allowing for the calculation of the spectral density for solvable models are determined. A linear Ising model is taken…
In this paper we expose the results of our recent work on the dynamical TAP approach to mean field glassy systems. Our aim is to clarify the connection between free energy landscape and out of equilibrium dynamics in solvable models.…
We investigate the spin and charge densities of surface states of the three-dimensional topological insulator $Bi_2Se_3$, starting from the continuum description of the material [Zhang {\em et al.}, Nat. Phys. 5, 438 (2009)]. The spin…
As spin glass materials have extremely slow dynamics, devious numerical methods are needed to study low-temperature states. A simple and fast optimization version of the classical Kasteleyn treatment of the Ising model is described and…