Related papers: The free and freer XY models
We consider 3D active plane rotators, where the interaction between the spins is of XY-type and where each spin is driven to rotate. For the clock-model, when the spins take N\gg1 possible values, we conjecture that there are two…
An $XY$ model, generalized by inclusion of up to an infinite number of higher-order pairwise interactions with an exponentially decreasing strength, is studied by spin-wave theory and Monte Carlo simulations. At low temperatures the model…
We investigate a Hamiltonian model of networks. The model is a mirror formulation of the XY model (hence the name) -- instead letting the XY spins vary, keeping the coupling topology static, we keep the spins conserved and sample different…
We determine the arrangement of spins in the ground state of the XY model with quenched, random fields, on a fully connected graph. Two types of disordered fields are considered, namely randomly oriented magnetic fields, and randomly…
We investigate an XY spin-glass model in which both spins and interactions (or couplings) evolve in time, but with widely separated time-scales. For large times this model can be solved using replica theory, requiring two levels of…
The phase transition in the XY model on one-dimensional small-world networks is investigated by means of Monte-Carlo simulations. It is found that long-range order is present at finite temperatures, even for very small values of the…
We explore the generic long wavelength properties of an active XY model on a substrate, consisting of collection of nearly phase-ordered active XY spins in contact with a diffusing, conserved species, as a representative system of active…
We have considered a new type of 'XY' model where spins are placed on concentric ring with constant spin density in every ring. The spin executes continuous rotation under a modified Shore-Zwanzig Hamiltonian (J. Chem. Phys. 63, 5445…
We study the behavior of the classical XY model on a two-dimensional square lattice, with interactions occurring within a vision cone of each spin. Via Monte Carlo simulations, we explore one non-reciprocal and two reciprocal…
We study ring-exchange models for bosons or XY-spins on the triangular lattice. A four-spin exchange leads to a manifold of ground states with gapless excitations and critical power-law correlations. With a nearest-neighbour exchange,…
The unbinding of vortex-antivortex pairs for the classical two-dimensional XY model in a magnetic field is studied. A single such pair is connected by a string of overturned spins, leading to linear confinement. We show that this system…
A statistical mechanic study of the $XY$ model with nonlinear interaction is presented on bipartite sparse random graphs. The model properties are compared to those of the $p$-clock model, in which the planar continuous spins are…
We propose a thermodynamic multi-state spin model in order to describe equilibrial behavior of a society. Our model is inspired by the Axelrod model used in social network studies. In the framework of the statistical mechanics language, we…
We characterize the phase space for the infinite volume limit of a ferromagnetic mean-field XY model in a random field pointing in one direction with two symmetric values. We determine the stationary solutions and detect possible phase…
We investigate an XY spin-glass model in which both spins and couplings evolve in time: the spins change rapidly according to Glauber-type rules, whereas the couplings evolve slowly with a dynamics involving spin correlations and Gaussian…
We prove the existence of a finite temperature Z_{2} phase transition for the topological charge ordering within the Fully Frustrated XY Model. Our method enables a proof of the topological charge confinement within the conventional XY…
We study a zero-temperature phase transition in the random field Ising model on scale-free networks with the degree exponent $\gamma$. Using an analytic mean-field theory, we find that the spins are always in the ordered phase for…
We elucidate that the nearly phase-ordered active XY spins in contact with a conserved, diffusing species on a substrate can be stable. For wide-ranging model parameters, it has stable uniform phases robust against noises. These are…
We study random-field xy spin model at T=0 numerically on lattices of up to 1000 x 1000 x 1000 spins with the accent on the weak random field. Our numerical method is physically equivalent to slow cooling in which the system is gradually…
We study vortex unbinding for the classical two-dimensional XY model in a magnetic field on square and triangular lattices. A renormalization group analysis combined with duality in the model shows that at high temperature and high field,…