English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The two-dimensional ($2d$) fully frustrated Planar Rotator model on a squarelattice has been the subject of a long controversy due to the simultaneous$Z_2$ and $O(2)$ symmetry existing in the model. The $O(2)$ symmetry beingresponsible for the Berezinskii - Kosterlitz - Thouless transition ($BKT$)while the $Z_2$ drives an Ising-like transition. There are arguments supportingtwo possible scenarios, one advocating that the loss of $Ising$ and $BKT$ ordertake place at the same temperature $T_{t}$ and the other that the $Z_2$transition occurs at a higher temperature than the $BKT$ one. In the first casean 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 anaverage over the estimates taken about several of those quantities, it isdifficult to decide if they are describing the same or slightly separatetransitions. In this paper we describe an iterative method based on theknowledge of the complex zeros of the energy probability distribution to studythe critical behavior of the system. The method is general with advantages overmost conventional techniques since it does not need to identify any orderparameter \emph{a priori}. The critical temperature and exponents can beobtained with good precision. We apply the method to study the Fully FrustratedPlanar Rotator ($PR$) and the Anisotropic Heisenberg ($XY$) models in twodimensions. We show that both models are in a new universality class with$T_{PR}=0.45286(32)$ and $T_{XY}=0.36916(16)$ and the transition exponent$\nu=0.824(30)$ ($\frac{1}{\nu}=1.22(4)$).

The fully frustrated XY model revisited: A new universality class