Critical properties of the three-dimensional XY model in large-scale Monte-Carlo simulations

Jeon, Inho; Shin, Jong-Geun; Cha, Min-Chul

doi:10.3938/jkps.60.581

Cited by 2 publications

(1 citation statement)

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“…11, for ∆ = 0.25, that the susceptibility peak corresponding to m 3 at the transition N-P grows as χ 3 (T c ) ∼ L 1.955 , with T c ≃ 1.652, very close to the expected γ/ν ∼ 1.96 value. We also measured the helicity modulus whose behavior in the critical region is continuous [5,61,63,64] and given by Υ ∼ t υ , where υ is the critical exponent and t is the reduced temperature. Assuming the universal scaling function Υ(T, L) = L −υ/ν g(tL 1/ν ), and using the scaling law υ/ν = d − 2 = 1 [5,61], LΥ(T c , L) = g(0) must be independent of the system size at the transition.…”

Section: B 3dmentioning

confidence: 99%

Competing nematic interactions in a generalizedXYmodel in two and three dimensions

2016

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We study a generalization of the XY model with an additional nematic-like term through extensive numerical simulations and finite-size techniques, both in two and three dimensions. While the original model favors local alignment, the extra term induces angles of 2π/q between neighboring spins. We focus here on the q = 8 case (while presenting new results for other values of q as well) whose phase diagram is much richer than the well-known q = 2 case. In particular, the model presents not only continuous, standard transitions between Berezinskii-Kosterlitz-Thouless (BKT) phases as in q = 2, but also infinite-order transitions involving intermediate, competition-driven phases absent for q = 2 and 3. Besides presenting multiple transitions, our results show that having vortices decoupling at a transition is not a sufficient condition for it to be of BKT type.

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