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Two-dimensional XY and clock models studied via the dynamics generated by rough surfaces.

A Faissal Brito¹, José Arnaldo Redinz, J A Plascak

¹Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, CP 702, 30123-970, Belo Horizonte, MG, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 7, 2010

Summary

This study investigates the p-state clock model using Monte Carlo simulations. For p>=5, it reveals a Berezinskii-Kosterlitz-Thouless transition at high temperatures and a first-order transition at low temperatures.

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Area of Science:

Statistical Mechanics
Condensed Matter Physics
Computational Physics

Background:

The p-state clock model is a fundamental model in statistical mechanics.
Understanding phase transitions in magnetic systems is crucial for materials science.

Purpose of the Study:

To investigate the phase transitions of the p-state clock model for general p values.
To characterize high-temperature and low-temperature phase transitions using a novel simulation approach.

Main Methods:

Monte Carlo simulations with heat-bath single spin flipping.
Mapping spin configurations to a solid-on-solid growth model.
Calculation of growth exponents from kinetic roughening dynamics.

Main Results:

Growth exponents were calculated for the kinetic roughening surface.
For p>=5, the high-temperature phase transition is identified as Berezinskii-Kosterlitz-Thouless (BKT).
The low-temperature phase transition for p>=5 exhibits first-order characteristics.

Conclusions:

The employed simulation method effectively characterizes equilibrium magnetic properties.
The high-temperature BKT transition for p>=5 matches the XY model.
The study provides insights into the nature of phase transitions in the p-state clock model.