Multicanonical sampling of the space of states of ℋ(2, n)-vector models

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. * shevchenko.ya@dvfu.ru † makarov.ag@dvfu.ru ‡

Low-energy states, ground states, and variable frustrations of the finite-size dipolar Cairo lattices

“…The existence of clusters of a low-energy phase, cluster formation, the emergence of a "percolation cluster," i.e., the processes of merging into one large cluster the connection of clusters (domains) of the ground state with thermodynamics, were discussed for artificial superspin ice in Refs. [29,30], and for macrospin glass in Ref. [71].…”

“…The study of the thermodynamic states of bulk spin ice to investigate the phenomenon of frustration and to study in detail the configurations of bulk magnets is associated with well-known experimental difficulties. Therefore, researchers often prefer two-dimensional (2D) analogs for studying the statistical mechanics of Ising-like frustrated spin systems on lattices with specific geometry, including those not observed in nature [29][30][31].…”

“…There are many approaches to obtaining an approximate solution of the Ising model; see, for example, [17,30,[45][46][47][48][49]. The exact calculation of the ground-state energy even for a classical Ising spin glass on a 2D lattice with the nearestneighbor interaction is a computationally difficult problem, or even NP-complete [41].…”

Multispin Monte Carlo Method

“…Достоверность результатов была проверена и подтверждена путем сравнения данных, полученных с помощью гибридного метода, с данными, полученными с помощью аналитического решения 2D модели Изинга без внешнего поля, опубликованного в работе [13]. Авторами не только были повторены результаты, опубликованные в работе [6]. Показано, см.…”

“…Позже появились алгоритмы, использующие гистограммные техники. Например, метод Ванга -Ландау (Wang -Landau) [5,6]. Данный метод принадлежит классу энтропийных алгоритмов и позволяет напрямую рассчитывать плотность состояний G(E).…”