Zero-temperature transition and correlation-length exponent of the frustratedXYmodel on a honeycomb lattice

Abstract

Phase coherence and vortex order in the fully frustrated XY model on a two-dimensional honeycomb lattice are studied by extensive Monte Carlo simulations using the parallel tempering method and finite-size scaling. No evidence is found for an equilibrium order-disorder or a spin/vortex-glass transition, suggested in previous simulation works. Instead, the scaling analysis of correlations of phase and vortex variables in the full equilibrated system is consistent with a phase transition where the critical temperature vanishes and the correlation lengths diverge as a power law with decreasing temperatures and corresponding critical exponents ν ph and ν v . This behavior and the near agreement of the critical exponents suggest a zero-temperature transition scenario where phase and vortex variables remain coupled on large length scales.

Resistive transition in frustrated Josephson-junction arrays on a honeycomb lattice

“…The best data collapse provides an estimate of the critical exponent ν = 1.40 (9). The data collapse is achieved quantitatively by means of a least-squares fit method 19,28 , varying the parameter ν. The scaling function g(x) is approximated by a Taylor series expansion for small x, truncated beyond 4th order, which is used to fit the data and provide the least-square residuals.…”

“…However, the question of the resistive transition was not investigated. In a recent MC study of phase coherence in the fully frustrated XY model a zero-temperature transition scenario 19 was proposed, where T c = 0 but the divergent correlation length, ξ ∝ T −ν , should lead to measurable effects at finite temperatures in the linear and nonlinear resistivity, determined by the thermal critical exponent ν. So far, a direct calculation of the resistive behavior of JJ arrays on a honeycomb lattice and comparison to experiments have not been presented.…”

Superconductor-insulator transition of Josephson-junction arrays on a honeycomb lattice in a magnetic field

“…Since the quantum phase transition can be described by a (2+1)-dimensional classical model, one thus should expect a first order transition for f = 1/3. On the other hand, for f = 1/2, similar arguments suggest that the vortex order should be described by an antiferromagnetic Ising model on a triangular lattice 29 . This Ising model is geometrically frustrated and has a highly degenerate ground state but shows a continuous phase transition in 3 dimensions, as a layered triangular lattice 46 .…”

“…The same system fabricated to be uniformly thick 20 is not described by the present model, which assumes superconducting "grains" and weak links on a length scale of nanohole size and should belong to a different universality. The f = 1/2 case is of particular interest since geometrical frustration combined with thermal fluctuations leads to an unusual phase transition as a function of temperature 17,25,26,29 . It should be of interest to investigate the effects of geometrical disorder in the quantum transition of this system 15,22,43 .…”

Ordered phases and phase transitions in the fully frustratedXYmodel on a honeycomb lattice

“…The available numerical data 12,[15][16][17][18] does not lead to a unique conclusion and allows for different interpretations, including the existence of a spin-glass transition. 17 In this work we reexamine the fully frustrated XY model on a honeycomb lattice with the aim of finding an answer to this question, as well as establishing what is the nature of the phase transition (transitions) induced by the positiveness of f DW .…”