We study the phase diagram and critical behaviour of the two- dimensional square-lattice fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau–Ginzburg–Wilson Hamiltonian for the critical modes of the FFXY model, and a coupled Ising XY model. We present a finite-size-scaling analysis of the results of high-precision Monte Carlo simulations on L × L square lattices, up to L = O(103 ). In the FFXY model and in the other models, when the transitions are continuous, there are two very close but separate transitions. There is an Ising chiral transition characterized by the onset of chiral long-range order while spins remain paramagnetic. Then, as temperature decreases, the systems undergo a Kosterlitz–Thouless spin transition to a phase with quasi-long-range order. The FFXY model and the other models, in a rather large parameter region, show a crossover behaviour at the chiral and spin transitions that is universal to some extent. We conjecture that this universal behaviour is due to a multicritical point. The numerical data suggest that the relevant multicritical point is a zero- temperature transition. A possible candidate is the O(4) point that controls the low-temperature behaviour of the 4-vector model.

Multicritical behaviour in the fully frustrated XY model and related systems / Hasenbusch, M; Pelissetto, Andrea; Vicari, E.. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - STAMPA. - -:(2005), p. P12002. [10.1088/1742-5468/2005/12/P12002]

Multicritical behaviour in the fully frustrated XY model and related systems

PELISSETTO, Andrea;
2005

Abstract

We study the phase diagram and critical behaviour of the two- dimensional square-lattice fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau–Ginzburg–Wilson Hamiltonian for the critical modes of the FFXY model, and a coupled Ising XY model. We present a finite-size-scaling analysis of the results of high-precision Monte Carlo simulations on L × L square lattices, up to L = O(103 ). In the FFXY model and in the other models, when the transitions are continuous, there are two very close but separate transitions. There is an Ising chiral transition characterized by the onset of chiral long-range order while spins remain paramagnetic. Then, as temperature decreases, the systems undergo a Kosterlitz–Thouless spin transition to a phase with quasi-long-range order. The FFXY model and the other models, in a rather large parameter region, show a crossover behaviour at the chiral and spin transitions that is universal to some extent. We conjecture that this universal behaviour is due to a multicritical point. The numerical data suggest that the relevant multicritical point is a zero- temperature transition. A possible candidate is the O(4) point that controls the low-temperature behaviour of the 4-vector model.
2005
01 Pubblicazione su rivista::01a Articolo in rivista
Multicritical behaviour in the fully frustrated XY model and related systems / Hasenbusch, M; Pelissetto, Andrea; Vicari, E.. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - STAMPA. - -:(2005), p. P12002. [10.1088/1742-5468/2005/12/P12002]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/74978
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