Critical behavior of two-dimensional frustrated spin models with noncollinear order

Calabrese, Pasquale; Parruccini, Pietro

doi:10.1103/physrevb.64.184408

Cited by 18 publications

(12 citation statements)

References 83 publications

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“…Even though we have found no evidence for it, our results do not necessarily contradict those of Ref. [25]. It is possible that the models we have considered are outside the attraction domain of the FT fixed point.…”

Section: Resultscontrasting

confidence: 63%

Critical behavior of two-dimensional fully frustrated XY systems

Hasenbusch

Pelissetto

Vicari

2006

J. Phys.: Conf. Ser.

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We study the phase diagram of the two-dimensional 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 Monte Carlo simulations on square lattices L × L, L 10 3 . We show that the lowtemperature phase of these models is controlled by the same line of Gaussian fixed points as in the standard XY model. We find that, if a model undergoes a unique transition by varying temperature, then the transition is of first order. In the opposite case we observe two very close transitions: a transition associated with the spin degrees of freedom and, as temperature increases, a transition where chiral modes become critical. If they are continuous, they belong to the Kosterlitz-Thouless and to the Ising universality class, respectively. Ising and Kosterlitz-Thouless behavior is observed only after a preasymptotic regime, which is universal to some extent. In the chiral case, the approach is nonmonotonic for most observables, and there is a wide region in which finite-size scaling is controlled by an effective exponent ν eff ≈ 0.8. This explains the result ν ≈ 0.8 of many previous studies using smaller lattices.

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Section: Resultscontrasting

confidence: 63%

Critical behavior of two-dimensional fully frustrated XY systems

Hasenbusch

Pelissetto

Vicari

2006

J. Phys.: Conf. Ser.

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“…Thus, our results do not support the field-theoretical results of Refs. [70,65], which provided some evidence for the existence of a stable fixed point in the RG flow of the LGW continuous theory (5). However, they are not necessarily in contradiction, since the lattice models considered here may be outside the attraction domain of the stable fixed point found in Refs.…”

Section: Discussionmentioning

confidence: 50%

Multicritical behaviour in the fully frustratedXYmodel and related systems

Pelissetto²,

2005

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Abstract. We study the phase diagram and critical behavior 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 square lattices L × L, up to L = O(10 3 ). 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 behavior at the chiral and spin transitions that is universal to some extent. We conjecture that this universal behavior 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 behavior of the 4-vector model.Multicritical behavior in the fully frustrated XY model and related systems 2

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“…Note that, within these FD approaches, one also finds a fixed point in d =2 with nontrivial critical exponents in the N = 2 and N =3 cases. 31,33,34 This fact has led to the hypothesis of a Kosterlitz-Thouless-type behavior induced by Z 2 topological defects for Heisenberg spins. 33 The second explanation is based on both the ⑀ =4−d ͑or pseudo-⑀͒ expansion [35][36][37] and the nonperturbative RG ͑NPRG͒ approaches.…”

Section: Introductionmentioning

confidence: 99%

“…31,33,34 This fact has led to the hypothesis of a Kosterlitz-Thouless-type behavior induced by Z 2 topological defects for Heisenberg spins. 33 The second explanation is based on both the ⑀ =4−d ͑or pseudo-⑀͒ expansion [35][36][37] and the nonperturbative RG ͑NPRG͒ approaches. 1,[38][39][40][41] In these approaches, one finds that there exists, within the ͑d , N͒ plane, a line N c ͑d͒ that separates a second-order region for N Ͼ N c from a first-order region for N Ͻ N c .…”

Section: Introductionmentioning

confidence: 99%

“…44 relies on the presence of nonanalytic contributions to the ␤ function at the fixed point. 45 The same kind of problem has been mentioned in the case of frustrated magnets 33,34 but it was assumed to leave unaffected the qualitative predictions, in particular, the existence of a nontrivial fixed point in the Heisenberg case. We show here, on the contrary, that the phenomenon of apparent convergence toward erroneous values, together with the presence of instabilities of some critical exponents with respect to the resummation parameters, leads to seriously question the conclusions drawn in the past as for the critical behavior of these systems.…”

Section: Introductionmentioning

confidence: 99%

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Relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions

et al. 2010

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We show that the critical behavior of two-and three-dimensional frustrated magnets cannot reliably be described from the known five-and six-loop perturbative renormalization-group results. Our conclusions are based on a careful reanalysis of the resummed perturbative series obtained within the zero-momentum massive scheme. In three dimensions, the critical exponents for XY and Heisenberg spins display strong dependences on the parameters of the resummation procedure and on the loop order. This behavior strongly suggests that the fixed points found are in fact spurious. In two dimensions, we find, as in the O͑N͒ case, that there is apparent convergence of the critical exponents but toward erroneous values. As a consequence, the interesting question of the description of the crossover/transition induced by Z 2 topological defects in two-dimensional frustrated Heisenberg spins remains open.

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Critical behavior of two-dimensional frustrated spin models with noncollinear order

Cited by 18 publications

References 83 publications

Critical behavior of two-dimensional fully frustrated XY systems

Critical behavior of two-dimensional fully frustrated XY systems

Multicritical behaviour in the fully frustratedXYmodel and related systems

Relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions

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