Critical behavior of frustrated systems: Monte Carlo simulations versus Renormalization Group

We study the critical behavior of frustrated systems by means of Pade-Borel resummed three-loop renormalization-group expansions and numerical Monte Carlo simulations. Amazingly, for six-component spins where the transition is second order, both approaches disagree. This unusual situation is analyzed both from the point of view of the convergence of the resummed series and from the possible relevance of non perturbative effects.Comment: RevTex, 10 pages, 3 Postscript figure

A characterization of those automata that structurally generate finite groups

Antonenko and Russyev independently have shown that any Mealy automaton with no cycles with exit--that is, where every cycle in the underlying directed graph is a sink component--generates a fi- nite (semi)group, regardless of the choice of the production functions. Antonenko has proved that this constitutes a characterization in the non-invertible case and asked for the invertible case, which is proved in this paper

Spin Stiffness of Stacked Triangular Antiferromagnets

We study the spin stiffness of stacked triangular antiferromagnets using both heat bath and broad histogram Monte Carlo methods. Our results are consistent with a continuous transition belonging to the chiral universality class first proposed by Kawamura.Comment: 5 pages, 7 figure

Monte Carlo renormalization group study of the Heisenberg and XY antiferromagnet on the stacked triangular lattice and the chiral ϕ4\phi^4 model

With the help of the improved Monte Carlo renormalization-group scheme, we numerically investigate the renormalization group flow of the antiferromagnetic Heisenberg and XY spin model on the stacked triangular lattice (STA-model) and its effective Hamiltonian, 2N-component chiral $\phi^4$ model which is used in the field-theoretical studies. We find that the XY-STA model with the lattice size $126\times 144 \times 126$ exhibits clear first-order behavior. We also find that the renormalization-group flow of STA model is well reproduced by the chiral $\phi^4$ model, and that there are no chiral fixed point of renormalization-group flow for N=2 and 3 cases. This result indicates that the Heisenberg-STA model also undergoes first-order transition.Comment: v1:15 pages, 15 figures v2:updated references v3:added comments on the higher order irrelevant scaling variables v4:added results of larger sizes v5:final version to appear in J.Phys.Soc.Jpn Vol.72, No.

Chiral phase transitions: focus driven critical behavior in systems with planar and vector ordering

The fixed point that governs the critical behavior of magnets described by the $N$-vector chiral model under the physical values of $N$ ($N =2, 3$) is shown to be a stable focus both in two and three dimensions. Robust evidence in favor of this conclusion is obtained within the five-loop and six-loop renormalization-group analysis in fixed dimension. The spiral-like approach of the chiral fixed point results in unusual crossover and near-critical regimes that may imitate varying critical exponents seen in physical and computer experiments.Comment: 4 pages, 5 figures. Discussion enlarge

Field-theory results for three-dimensional transitions with complex symmetries

We discuss several examples of three-dimensional critical phenomena that can be described by Landau-Ginzburg-Wilson $\phi^4$ theories. We present an overview of field-theoretical results obtained from the analysis of high-order perturbative series in the frameworks of the $\epsilon$ and of the fixed-dimension d=3 expansions. In particular, we discuss the stability of the O(N)-symmetric fixed point in a generic N-component theory, the critical behaviors of randomly dilute Ising-like systems and frustrated spin systems with noncollinear order, the multicritical behavior arising from the competition of two distinct types of ordering with symmetry O($n_1$) and O($n_2$) respectively.Comment: 9 pages, Talk at the Conference TH2002, Paris, July 200

Critical behavior of O(2)xO(N) symmetric models

We investigate the controversial issue of the existence of universality classes describing critical phenomena in three-dimensional statistical systems characterized by a matrix order parameter with symmetry O(2)xO(N) and symmetry-breaking pattern O(2)xO(N) -> O(2)xO(N-2). Physical realizations of these systems are, for example, frustrated spin models with noncollinear order. Starting from the field-theoretical Landau-Ginzburg-Wilson Hamiltonian, we consider the massless critical theory and the minimal-subtraction scheme without epsilon expansion. The three-dimensional analysis of the corresponding five-loop expansions shows the existence of a stable fixed point for N=2 and N=3, confirming recent field-theoretical results based on a six-loop expansion in the alternative zero-momentum renormalization scheme defined in the massive disordered phase. In addition, we report numerical Monte Carlo simulations of a class of three-dimensional O(2)xO(2)-symmetric lattice models. The results provide further support to the existence of the O(2)xO(2) universality class predicted by the field-theoretical analyses.Comment: 45 pages, 20 figs, some additions, Phys.Rev.B in pres

Слабка збіжність сім'ї напівмарковських процесів до дифузійного процесу

Наведено основні критерії слабкої збіжності сім'ї напівмарковських процесів до ''чисто'' дифузійного процесу в умовах балансу та до дифузійного процесу Орнштейна–Уленбека за умови, що величина стрибка залежить від параметра серії ε.Приведены основные критерии слабой сходимости семейства полумарковских процессов к ''чисто'' диффузионному процессу в условиях баланса и к диффузионному процессу Орнштейна–Уленбека при условии, что величина скачка зависит от параметра серии ε.The basic criteria of weak convergence of a family of semi-Markov processes to the ''pure'' diffusion process under balance conditions and to the Ornstein–Uhlenbeck diffusion process provided that the value of jump depends on the series parameter ε are obtained

Chiral critical behavior in two dimensions from five-loop renormalization-group expansions

We analyse the critical behavior of two-dimensional N-vector spin systems with noncollinear order within the five-loop renormalization-group approximation. The structure of the RG flow is studied for different N leading to the conclusion that the chiral fixed point governing the critical behavior of physical systems with N = 2 and N = 3 does not coincide with that given by the 1/N expansion. We show that the stable chiral fixed point for $N \le N^*$, including N = 2 and N = 3, turns out to be a focus. We give a complete characterization of the critical behavior controlled by this fixed point, also evaluating the subleading crossover exponents. The spiral-like approach of the chiral fixed point is argued to give rise to unusual crossover and near-critical regimes that may imitate varying critical exponents seen in numerous physical and computer experiments.Comment: 17 pages, 12 figure

The critical behavior of frustrated spin models with noncollinear order

We study the critical behavior of frustrated spin models with noncollinear order, including stacked triangular antiferromagnets and helimagnets. For this purpose we compute the field-theoretic expansions at fixed dimension to six loops and determine their large-order behavior. For the physically relevant cases of two and three components, we show the existence of a new stable fixed point that corresponds to the conjectured chiral universality class. This contradicts previous three-loop field-theoretical results but is in agreement with experiments.Comment: 4 pages, RevTe