Phase transitions in two-dimensional uniformly frustrated XY spin systems

Phase Transition in Frustrated Magnetic Thin Film-Physics at Phase Boundaries

In this review, we outline some principal theoretical knowledge of the properties of frustrated spin systems and magnetic thin films. The two points we would like to emphasize: (i) the physics in low dimensions where exact solutions can be obtained; (ii) the physics at phase boundaries where interesting phenomena can occur due to competing interactions of the two phases around the boundary. This competition causes a frustration. We will concentrate our attention on magnetic thin films and phenomena occurring near the boundary of two phases of different symmetries. Two-dimensional (2D) systems are in fact the limiting case of thin films with a monolayer. Naturally, we will treat this case at the beginning. We begin by defining the frustration and giving examples of frustrated 2D Ising systems that we can exactly solve by transforming them into vertex models. We will show that these simple systems already contain most of the striking features of frustrated systems such as the high degeneracy of the ground state (GS), many phases in the GS phase diagram in the space of interaction parameters, the reentrance occurring near the boundaries of these phases, the disorder lines in the paramagnetic phase, and the partial disorder coexisting with the order at equilibrium. Thin films are then presented with different aspects: surface elementary excitations (surface spin waves), surface phase transition, and criticality. Several examples are shown and discussed. New results on skyrmions in thin films and superlattices are also displayed. By the examples presented in this review we show that the frustration when combined with the surface effect in low dimensions gives rise to striking phenomena observed in particular near the phase boundaries.

Kosterlitz-Thouless physics: a review of key issues

This article reviews, from a very personal point of view, the origins and the early work on transitions driven by topological defects such as vortices in the two dimensional planar rotor model and in (4)Helium films and dislocations and disclinations in 2D crystals. I cover the early papers with David Thouless and describe the important insights but also the errors and oversights since corrected by other workers. I then describe some of the experimental verifications of the theory and some numerical simulations. Finally applications to superconducting arrays of Josephson junctions and to recent cold atom experiments are described.

First-order transition in the XY model on a fully frustrated simple cubic lattice

We study the nature of the phase transition in the fully frustrated simple cubic lattice with the XY spin model. This system is the Villain's model generalized in three dimensions. The ground state is very particular with a 12-fold degeneracy. Previous studies have shown unusual critical properties. With the powerful Wang-Landau flat-histogram Monte Carlo method, we carry out in this work intensive simulations with very large lattice sizes. We show that the phase transition is clearly of first order, putting an end to the uncertainty which has lasted for more than 20 years.

Spin rotation technique for non-collinear magnetic systems: application to the generalized Villain model

This work develops a generalized technique for determining the static and dynamic properties of any non-collinear magnetic system. By rotating the spin operators into the local spin reference frame, we evaluate the zeroth, first, and second order terms in a Holstein-Primakoff expansion, and through a Green's functions approach, we determine the structure factor intensities for the spin-wave frequencies. To demonstrate this technique, we examine the spin-wave dynamics of the generalized Villain model with a varying interchain interaction. The new interchain coupling expands the overall phase diagram with the realization of two non-equivalent canted spin configurations. The rotational Holstein-Primakoff expansion provides both analytical and numerical results for the spin dynamics and intensities of these phases.

Splitting the voter Potts model critical point

Recently some two-dimensional models with double symmetric absorbing states were shown to share the same critical behavior that was called the voter universality class. We show that, for an absorbing-states Potts model with finite but further than nearest-neighbor range of interactions, the critical point is split into two critical points: one of the Ising type and the other of the directed percolation universality class. Similar splitting takes place in the three-dimensional nearest-neighbor model.

Critical behavior of the frustrated antiferromagnetic six-state clock model on a triangular lattice

We study the antiferromagnetic six-state clock model with nearest neighbor interactions on a triangular lattice with extensive Monte Carlo simulations. We find clear indications of two phase transitions at two different temperatures: Below T(I) a chirality order sets in and by a thorough finite-size-scaling analysis of the specific heat and the chirality correlation length we show that this transition is in the Ising universality class (with a nonvanishing chirality order parameter below T(I)). At T(KT) (<T(I)) the spin-spin correlation length as well as the spin susceptibility diverges according to a Kosterlitz-Thouless (KT) form and spin correlations decay algebraically below T(KT). We compare our results to recent x-ray diffraction experiments on the orientational ordering of CF3Br monolayers physisorbed on graphite. We argue that the six-state clock model describes the universal feature of the phase transition in the experimental system and that the orientational ordering belongs to the KT universality class.

Nonequilibrium transitions in fully frustrated Josephson junction arrays

We study the effect of thermal fluctuations in a fully frustrated Josephson junction array driven by a current I larger than the apparent critical current I(c)(T). We calculate numerically the behavior of the chiral order parameter of Z2 symmetry and the transverse helicity modulus [related to the U(1) symmetry] as a function of temperature. We find that the Z2 transition occurs at a temperature T(Z2)(I) which is lower than the temperature T(U(1))(I) for the U(1) transition. Both transitions could be observed experimentally from measurements of the longitudinal and transverse voltages.