Short-Range Berezinskii-Kosterlitz-Thouless Phase Characterization for the q-State Clock Model.

Oscar A Negrete,Eugenio E Vogel,Francisco J Peña,Patricio Vargas,Gonzalo Saravia

doi:10.3390/e23081019

Oscar A Negrete, Eugenio E Vogel + Show 3 more

Open Access

https://doi.org/10.3390/e23081019

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Abstract

Beyond the usual ferromagnetic and paramagnetic phases present in spin systems, the usual q-state clock model presents an intermediate vortex state when the number of possible orientations q for the system is greater than or equal to 5. Such vortex states give rise to the Berezinskii-Kosterlitz-Thouless (BKT) phase present up to the XY model in the limit . Based on information theory, we present here an analysis of the classical order parameters plus new short-range parameters defined here. Thus, we show that even using the first nearest neighbors spin-spin correlations only, it is possible to distinguish the two transitions presented by this system for q greater than or equal to 5. Moreover, the appearance at relatively low temperature and disappearance of the BKT phase at a rather fix higher temperature is univocally determined by the short-range interactions recognized by the information content of classical and new parameters.

Highlights

The idea of using simple, discrete, and finite models to understand complex phenomena is a fundamental part of statistical physics
MD measures the way the magnetization loses its dominant direction originated in the spontaneous ergodicity breaking associated to the ferromagnetic phase (FP)-BKT phase transition only, as defined at the end of Section 2. This figure offers a complete picture of the magnetization evolution of the system as T increases: at low-temperature, ergodicity is broken in favor of a ferromagnetic ordering along one dominant direction; the FP is lost as drastically shown by the abrupt descent of mD; at T increases the absolute magnetization, C20 and C30 point to the presence of short magnetic ordering, with ergodicity recovering with the increase of T; At a temperature in which the slightest short-range interaction is exceeded by the thermal fluctuations the paramagnetic phase (PP) is reached and ergodicity is fully recovered
Information content of the series corresponding to the classical variables internal energy and magnetization recognize the different phase transitions present in the clock model

Summary

Introduction

The idea of using simple, discrete, and finite models to understand complex phenomena is a fundamental part of statistical physics. A simple model that exhibits many of these fascinating features is the so-called q-state clock model, which is a discretized XY [11,12,13] spin model defined on the square lattice We recently solved this model exactly for a very small system [14] and on larger lattices up to square lattices 128 × 128 by Monte Carlo simulations, showing clearly the two-phase transitions and using two information theory approaches (mutability and diversity) and calculated in thermal equilibrium on the thermodynamic energy and magnetization variables as functions of temperature. One of the main purposes of this work is to show that both phase transitions can be characterized by appropriate short-range order parameters defined below, using simple spin correlations up to second and third nearest neighbors.

System

Calculations and Data Organization

Information Recognizer

Short-Range Order Parameters

Results and Discussion

Conclusions