186,156 research outputs found
Five-loop epsilon expansion for O (n) X O (m) spin models
No full textWe compute the renormalization group functions of a Landau-Ginzburg-Wilson Hamiltonian with O(n) x O(m) symmetry up to five-loop in minimal subtraction scheme. The line n(+)(m, d), which limits the region of second-order phase transition, is reconstructed in the framework of the epsilon = 4 - d expansion for generic values of m up to O(epsilon(5)). For the physically interesting case of noncollinear but planar orderings (m = 2) we obtain n(+)(2, 3) = 6.1(6) by exploiting different resummation procedures. We substantiate this results reanalyzing six-loop fixed dimension series with pseudo-epsilon expansion, obtaining n(+)(2, 3) = 6.22(12). We also provide predictions for the critical exponents characterizing the second-order phase transition occurring for n > n(+). (C) 2003 Elsevier B.V. All rights reserved
Critical behavior of two-dimensional frustrated spin models with noncollinear order (vol 64, art no 184408, 2001)
No full textFive-loop epsilon expansion for U(n) x U(m) models: finite-temperature phase transition in light QCD
No full textWe consider the U(n) x U(m) symmetric Phi(4) lagrangian to describe the finite-temperature phase transition in QCD in the limit of vanishing quark masses with n=M=N(f) flavors and unbroken anomaly at T(c). We compute the Renormalization Group functions to five-loop order in Minimal Subtraction scheme. Such higher order functions allow to describe accurately the three-dimensional fixed-point structure in the plane (n, m), and to reconstruct the line n(+) (m, d) which limits the region of second-order phase transitions by an expansion in epsilon=4-d. We always find n(+) (m, 3)>m, thus no three-dimensional stable fixed point exists for n=m and the finite temperature transition in light QCD should be first-order. This result is confirmed by the pseudo-epsilon analysis of massive six-loop three dimensional series
Harmonic crossover exponents in O(n) models with the pseudo-epsilon expansion approach
No full textWe determine the crossover exponents associated with the traceless tensorial quadratic field and the third- and fourth-harmonic operators for O(n) vector models by reanalyzing the existing six-loop fixed-dimension series with the pseudo-epsilon expansion. With this approach we obtain accurate theoretical estimates that are in optimum agreement with other theoretical and experimental results
Crossover behavior in three-dimensional dilute spin systems
No full textWe study the crossover behaviors that can be observed in the high-temperature
phase of three-dimensional dilute spin systems, using a field-theoretical
approach. In particular, for randomly dilute Ising systems we consider the
Gaussian-to-random and the pure-Ising-to-random crossover, determining the
corresponding crossover functions for the magnetic susceptibility and the
correlation length. Moreover, for the physically interesting cases of dilute
Ising, XY, and Heisenberg systems, we estimate several universal ratios of
scaling-correction amplitudes entering the high-temperature Wegner expansion of
the magnetic susceptibility, of the correlation length, and of the
zero-momentum quartic couplings
Critical thermodynamics of a three-dimensional chiral model for N > 3
No full textThe critical behavior of the three-dimensional N-vector chiral model is studied for arbitrary N. The known six-loop renormalization-group (RG) expansions are resummed using the Borel transformation combined with the conformal mapping and Pade approximant techniques. Analyzing the fixed-point location and the structure of RG flows, it is found that two marginal values of N exist which separate domains of continuous chiral phase transitions N>N-c1 and NN>N-c2 where such transitions are first order. Our calculations yield N-c1=6.4(4) and N-c2=5.7(3). For N>N-c1 the structure of RG flows is identical to that given by the epsilon and 1/N expansions with the chiral fixed point being a stable node. For N<N-c2 the chiral fixed point turns out to be a focus having no generic relation to the stable fixed point seen at small epsilon and large N. In this domain, containing the physical values N=2 and N=3, phase trajectories approach the fixed point in a spiral-like manner giving rise to unusual crossover regimes which may imitate varying (scattered) critical exponents seen in numerous physical and computer experiments
Chiral phase transitions: Focus driven critical behavior in systems with planar and vector ordering
No full textThe 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 spirallike 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
On the evaluation of the improvement parameter in the lattice Hamiltonian approach to critical phenomena
No full textCritical behavior of O(2)xO(N) symmetric models
No full textWe 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
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