Related papers: Active Spherical Model
The collective motion of self-driven agents is a phenomenon of great interest in interacting particle systems. In this paper, we develop and analyze a model of agent motion in one dimension with periodic boundaries using a stochastic…
A mean-field model of Ising spin glass with the Hamiltonian being a sum of the infinite-range ferromagnetic and random antiferromagnetic interactions is studied. It is shown that this model has phase transition in external magnetic field…
In this paper and in the companion one we address the problem of identifying the effective theory that describes the statistics of the fluctuations of what is thought to be the relevant order parameter for glassy systems---the overlap field…
We use quantum Monte Carlo methods and various analytic approximations to solve the Ising spin-glass model in a transverse field in the disordered phase. We focus on the behavior of the frequency dependent susceptibility of the system above…
We consider the thermal and athermal overdamped motion of particles in 1D geometries where discrete internal degrees of freedom (spin) are coupled with the translational motion. Adding a driving velocity that depends on the time-dependent…
We present the full phase diagram of the spherical $2+p$ spin glass model with $p\geq 4$. The main outcome is the presence of a new phase with both properties of Full Replica Symmetry Breaking (FRSB) phases of discrete models, e.g, the…
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…
We consider a system of hierarchical interacting spins under dynamics of spin-flip type with a ferromagnetic mean field interaction, scaling with the hierarchical distance, coupled with a system of linearly interacting hierarchical…
Spatio-temporal modelling is an increasingly popular topic in Statistics. Our paper contributes to this line of research by developing the theory, simulation and inference for a spatio-temporal Ornstein-Uhlenbeck process. We conduct…
We study the equilibrium and dynamical properties of a ferromagnetic spinor atomic Bose-Einstein condensate. In the vicinity of the critical point for a continuous quantum phase transition, universal behaviors are observed both in the…
Dynamic scaling analyses are performed in the spin-glass phase of the $\pm J$ Ising, the {\it XY}, and the Heisenberg models in three dimensions. We found a crossover from the critical dynamics to the ground-state dynamics in the Ising…
We present a theoretical framework that enables investigating rare transitions in a general model of an active particle in an external potential, with the thermal Active Ornstein-Uhlenbeck Particle (AOUP) appearing as a special case. Using…
We study a quantum extension of the spherical $p$-spin-glass model using the imaginary-time replica formalism. We solve the model numerically and we discuss two analytical approximation schemes that capture most of the features of the…
Inertial effects affecting both the translational and rotational dynamics are inherent to a broad range of active systems at the macroscopic scale. Thus, there is a pivotal need for proper models in the framework of active matter to…
The time-evolution of an Ising model with large driving fields over discrete time intervals is shown to be reproduced by an effective XXZ-Heisenberg model at leading order in the inverse field strength. For specific orientations of the…
Universality is key to the theory of phase transition stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour…
The critical behavior of a family of fully connected mean-field models with quenched disorder, the $M-p$ Ising spin glass, is analyzed, displaying a crossover between a continuous and a random first order phase transition as a control…
We introduce varying spin strengths to the Ising model, a central pillar of statistical physics. With inhomogeneous physical systems in mind, but also anticipating interdisciplinary applications, we present the model on network structures…
The name Ising has come to stand not only for a specific model, but for an entire universality class - arguably the most important such class - in the theory of critical phenomena. I review several examples, both in and out of equilibrium,…
Phase transitions, as one of the most intriguing phenomena in nature, are divided into first-order phase transitions (FOPTs) and continuous ones in current classification. While the latter shows striking phenomena of scaling and…