Related papers: Shattering in the Ising Pure $p$-Spin Model
The fractal dimensions and the percolation exponents of the geometrical spin clusters of like sign at criticality, are obtained numerically for an Ising model with temperature-dependent annealed bond dilution, also known as the thermalized…
At zero temperature, two-dimensional Ising spin glasses are known to fall into several universality classes. Here we consider the scaling at low but non-zero temperature and provide numerical evidence that $\eta \approx 0$ and $\nu \approx…
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…
Although SU(2) isospin symmetry is generally assumed in the basic theory of the strong interaction, a number of significant violations have been observed in scattering and bound states of nucleons. Many of these violations can be attributed…
We examine the behavior of the 2-spin spherical Sherrington-Kirkpatrick model with an external field by analyzing the overlap of a spin with the external field. Previous research has noted that, at low temperature, this overlap exhibits…
We study statistical characterization of the many-body states in exactly solvable models with internal degrees of freedom. The models under consideration include the isotropic and anisotropic Heisenberg spin chain, the Hubbard chain, and a…
We study the low-temperature spin-glass phases of the Sherrington-Kirkpatrick (SK) model and of the 3-dimensional short range Ising spin glass (3dISG). For the SK model, evidence for ultrametricity becomes clearer as the system size…
We study the Hopfield model where the ratio $\alpha$ of patterns to sites grows large. We prove that the free energy with inverse temperature $\beta$ and external field $B$ behaves like $\beta\sqrt\alpha+\gamma$, where $\gamma$ is the…
This work concerns the dynamical two-point spin correlation functions of the transverse Ising quantum chain at finite (non-zero) temperature, in the universal region near the quantum critical point. They are correlation functions of twist…
We study the spectrum of the Hessian of the Sherrington-Kirkpatrick model near T=0, whose eigenvalues are the masses of the bare propagators in the expansion around the mean-field solution. In the limit $T\ll 1$ two regions can be…
We have found a simple criterion which allows for the straightforward determination of the order-disorder critical temperatures. The method reproduces exactly results known for the two dimensional Ising, Potts and $Z(N<5)$ models. It also…
We study the coarsening model (zero-temperature Ising Glauber dynamics) on $\mathbb{Z}^d$ (for $d \geq 2$) with an asymmetric tie-breaking rule. This is a Markov process on the state space $\{-1,+1\}^{\mathbb{Z}^d}$ of "spin configurations"…
Suitable cluster definitions have allowed researchers to describe many ordering transitions in spin systems as geometric phenomena related to percolation. For spin glasses and some other systems with quenched disorder, however, such a…
Isothermal simulational data for the 3D Edwards-Anderson spin glass are collected at several temperatures below $T_{\rm c}$ and, in analogy with a recent model of dense colloidal suspensions,interpreted in terms of clusters of contiguous…
A kinetic one-dimensional Ising model is coupled to two heat baths, such that spins at even (odd) lattice sites experience a temperature $T_{e}$ ($% T_{o}$). Spin flips occur with Glauber-type rates generalised to the case of two…
We construct a model of short-range interacting Ising spins on a translationally invariant two-dimensional lattice that mimics a reversible circuit that multiplies or factorizes integers, depending on the choice of boundary conditions. We…
We present a large-scale simulation of the three-dimensional Ising spin glass with Gaussian disorder to low temperatures and large sizes using optimized population annealing Monte Carlo. Our primary focus is investigating the number of pure…
We study the scaling of entanglement in low-energy states of quantum many-body models on lattices of arbitrary dimensions. We allow for unbounded Hamiltonians such that systems with bosonic degrees of freedom are included. We show that if…
Using exact results, we determine the complex-temperature phase diagrams of the 2D Ising model on three regular heteropolygonal lattices, $(3 \cdot 6 \cdot 3 \cdot 6)$ (kagom\'{e}), $(3 \cdot 12^2)$, and $(4 \cdot 8^2)$ (bathroom tile),…
In this paper, the Glauber dynamics for the Ising model on the complete multipartite graph $K_{np_1,\dots,np_m}$ is investigated where $0<p_i<1$ is the proportion of the vertices in the $i$th component. We show that the dynamics exhibits…