Multicanonical Sampling of the Space of States of H(2,n)-Vector Models

TL;DR

This paper uses multicanonical sampling to analyze the thermodynamic properties of various Ising and spin models, revealing complex behaviors like multiple specific heat peaks and residual entropy, with new empirical schemes for state space partitioning.

Contribution

It introduces optimized multicanonical sampling schemes and explores thermodynamic phenomena in diverse spin models, including long-range interactions and quasilattices, highlighting novel properties.

Findings

Finite systems with long-range dipole interactions show multiple specific heat peaks.

No phase transition in nearest neighbor hexagonal lattice models, but singularity with long-range interactions.

Identification of a spin quasilattice with nonzero residual entropy.

Abstract

Problems of temperature behavior of specific heat are solved by the entropy simulation method for Ising models on a simple square lattice and a square spin ice (SSI) lattice with nearest neighbor interaction, models of hexagonal lattices with short-range (SR) dipole interaction, as well as with long-range (LR) dipole interaction and free boundary conditions, and models of spin quasilattices with finite interaction radius. It is established that systems of a finite number of Ising spins with LR dipole interaction can have unusual thermodynamic properties characterized by several specific-heat peaks in the absence of an external magnetic field. For a parallel multicanonical sampling method, optimal schemes are found empirically for partitioning the space of states into energy bands for Ising and SSI models, methods of concatenation and renormalization of histograms are discussed, and a flatness criterion of histograms is proposed. It is established that there is no phase transition in a model with nearest neighbor interaction on a hexagonal lattice, while the temperature behavior of specific heat exhibits singularity in the same model, in case of LR interaction. A spin quasilattice is found that exhibits a nonzero value of residual entropy.