Critical properties of a continuous family ofXYnoncollinear magnets

Abstract

Monte Carlo methods are used to study a family of three-dimensional XY frustrated models interpolating continuously between the stacked triangular antiferromagnets and a variant of this model for which a local rigidity constraint is imposed. Our study leads us to conclude that generically weak first order behavior occurs in this family of models in agreement with a recent nonperturbative renormalization group description of frustrated magnets.In spite of intensive study during the last 25 years the critical behavior of XY or Heisenberg frustrated magnets with a noncollinear ground state is still a strongly debated topic (see Refs. 1 and 2 and references therein). This is, for instance, the case of the celebrated XY Stacked Triangular Antiferromagnet (STA) that we consider here, whose Hamiltonian iswhere the S i are two-component vectors and the sum runs over all pairs of nearest neighbor spins on a stacked triangular lattice. In Eq.(1), the in-plane interactions are antiferromagnetic ͑J Ͻ 0͒ and the interplane interactions are taken to be ferromagnetic ͑J Ͼ 0͒ with ͉J͉ = 1. The competition between the in-plane antiferromagnetic interactions produces a ground state where the three spins S 1 , S 2 , and S 3 on each elementary triangular plaquette are oriented at 120°one to another, that is,For such a system, the order parameter is given by two orthogonal vectors of the same norm, a fact that has led to the hypothesis that noncollinear magnets could undergo a second order phase transition associated with a new-chiraluniversality class. 3 However, it is now becoming more and more widely accepted that the physics of frustrated magnets is not given by such a simple picture. 1,4-6 The complexity of the critical behavior of STA systems is exemplified in the experimental results (for a review see Ref. 1, and references therein). Indeed, scaling behavior is generally found while universality is violated since materials which belong, a priori, to the same universality class display different critical exponents. It is thus difficult to interpret the experimental data within the usual picture of critical phenomena.On the theoretical side, the situation is controversial. 1,5 A nonperturbative renormalization group (NPRG) method 1,4 finds that the phase transitions in these systems are generically weakly first order with the possibility of standard strongly first order transitions. More precisely while there is no RG fixed point there exists a whole region where the RG flow is very slow, corresponding to large-but finitecorrelation lengths at the transition, which allows one to compute pseudocritical exponents. Hence the violation of universality observed experimentally has a natural explanation since, in the absence of a fixed point, the pseudocritical exponents found depend on the microscopic Hamiltonians. On the other hand, Pelissetto et al. have derived and resummed the six-loop ␤ functions in three dimensions. 7 They find a fixed point and therefore predict a second order phase transition. Calabrese et al. have claimed tha...

Short-time dynamics of a family ofXYnoncollinear magnets

“…The values of β increase as r decreases in agreement with our previous study using equilibrium methods. 19,20 The value of β = 0.27(1) for r = 0 is slightly larger than that predicted by previous numerical studies but is consistent with the value obtained in experiments on STA XY antiferromagnets. 9 In summary, we have investigated the critical behavior of a family of XY noncollinear magnets on the stacked triangular lattice geometry using the short-time dynamics approach.…”

“…Finally, recent numerical studies of the STA model and its LGW formulation by Itakura 18 also indicate a first order phase transition for the STA XY model itself. In order to examine this effect of local rigidity in more detail, we introduced a generalized model in which we can continuously tune the local rigidity from the STA to the STAR limits 19,20 ,…”

Criticality in quantum triangular antiferromagnets via fermionized vortices

“…[23][24][25] Starting with Kawamura, several Monte Carlo simulations on the stacked triangular XY antiferromagnet conclude that the transition is continuous, [28][29][30][31] which also appears to be the case in our Monte Carlo simulations in the vicinity of the multicritical point. However, recent simulations on larger lattices claim a very weak first-order transition, 32,33 and simulations of modified XY systems expected to be in the same universality class have also seen a first-order transition. 33,34 On the other hand, Ref.…”

“…However, recent simulations on larger lattices claim a very weak first-order transition, 32,33 and simulations of modified XY systems expected to be in the same universality class have also seen a first-order transition. 33,34 On the other hand, Ref. 25 claims a continuous transition in the vicinity of the O͑4͒ fixed point in a model which is a lattice discretization of the action Eq.…”

Flat energy-histogram simulation of the phase transition in an Ising fully frustrated lattice

“…One of the most studied systems is the stacked triangular antiferromagnet (STA) with interaction between NN. This system with Ising [10], XY and Heisenberg spins [11,12] have been intensively studied since 1987 [13,14,15,16,17,18,19,20], but only recently that the 20-year controversy comes to an end [21,22,23,24,25,26,27,28,29,30]. Note that numerical simulations require now new efficient algorithms to deal with frustrated systems [29,30].…”