Generalized Crossover in multiparameter Hamiltonians

Many systems near criticality can be described by Hamiltonians involving several relevant couplings and possessing many nontrivial fixed points. A simple and physically appealing characterization of the crossover lines and surfaces connecting different nontrivial fixed points is presented. Generalized crossover is related to the vanishing of the RG function $Z_t^{-1}$. An explicit example is discussed in detail based on the tetragonal GLW Hamiltonian.Comment: 4 pages, 1figur

The critical behavior of 2-d frustrated spin models with noncollinear order

We study the critical behavior of frustrated spin models with noncollinear order in two dimensions, including antiferromagnets on a triangular lattice and fully frustrated antiferromagnets. For this purpose we consider the corresponding $O(N) \times O(2)$ Landau-Ginzburg-Wilson (LGW) Hamiltonian and compute the field-theoretic expansion to four loops and determine its large-order behavior. We show the existence of a stable fixed point for the physically relevant cases of two- and three-component spin models. We also give a prediction for the critical exponent $\eta$ which is $\eta =0.24(6)$ and $\eta =0.29(5)$ for N=3 and 2 respectively.Comment: 11 pages, 8 figure

On the evaluation of the improvement parameter in the lattice Hamiltonian approach to critical phenomena

In lattice Hamiltonian systems with a quartic coupling $\gamma$, a critical value $\gamma^*$ may exist such that, when $\gamma=\gamma^*$, the leading irrelevant operator decouples from the Hamiltonian and the leading nonscaling contribution to renormalization-group invariant physical quantities (evaluated in the critical region) vanishes. The 1/N expansion technique is applied to the evaluation of $\gamma^*$ for the lattice Hamiltonian of vector spin models with O(N) symmetry. As a byproduct, systematic asymptotic expansions for the relevant lattice massive one-loop integrals are obtained.Comment: Conclusions clarified; 26 pages, 6 figures, RevTeX

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