The Fully Frustrated XY Model Revisited: A New Universality Class View Full Text


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Article Info

DATE

2019-03-20

AUTHORS

A. B. Lima, L. A. S. Mól, B. V. Costa

ABSTRACT

The two-dimensional (2d) fully frustrated Planar Rotator model on a square lattice has been the subject of a long controversy due to the simultaneous Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z_2$$\end{document} and O(2) symmetry existing in the model. The O(2) symmetry being responsible for the Berezinskii–Kosterlitz–Thouless transition (BKT) while the Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z_2$$\end{document} drives an Ising-like transition. There are arguments supporting two possible scenarios, one advocating that the loss of Ising and BKT order take place at the same temperature Tt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{t}$$\end{document} and the other that the Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z_2$$\end{document} transition occurs at a higher temperature than the BKT one. In the first case an immediate consequence is that this model is in a new universality class. Most of the studies take hand of some order parameter like the stiffness, Binder’s cumulant or magnetization to obtain the transition temperature. Considering that the transition temperatures are obtained, in general, as an average over the estimates taken about several of those quantities, it is difficult to decide if they are describing the same or slightly separate transitions. In this paper we describe an iterative method based on the knowledge of the complex zeros of the energy probability distribution to study the critical behavior of the system. The method is general with advantages over most conventional techniques since it does not need to identify any order parameter a priori. The critical temperature and exponents can be obtained with good precision. We apply the method to study the Fully Frustrated Planar Rotator (FFPR) and the Anisotropic Heisenberg (FFXY) models in two dimensions. We show that both models are in a new universality class with TPR=0.45286(32)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{PR}=0.45286(32)$$\end{document} and TXY=0.36916(16)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{XY}=0.36916(16)$$\end{document} respectively and the transition exponent ν=0.824(30)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu =0.824(30)$$\end{document} (1ν=1.22(4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{\nu }=1.22(4)$$\end{document}). More... »

PAGES

960-971

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10955-019-02271-x

DOI

http://dx.doi.org/10.1007/s10955-019-02271-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112897475


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