14 research outputs found
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
Frustrated magnets in three dimensions: a nonperturbative approach
Frustrated magnets exhibit unusual critical behaviors: they display scaling
laws accompanied by nonuniversal critical exponents. This suggests that these
systems generically undergo very weak first order phase transitions. Moreover,
the different perturbative approaches used to investigate them are in conflict
and fail to correctly reproduce their behavior. Using a nonperturbative
approach we explain the mismatch between the different perturbative approaches
and account for the nonuniversal scaling observed.Comment: 7 pages, 1 figure. IOP style files included. To appear in Journal of
Physics: Condensed Matter. Proceedings of the conference HFM 2003, Grenoble,
Franc
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 -vector chiral model under the physical values of () 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
Universality classes of three-dimensional -vector model
We study the conditions under which the critical behavior of the
three-dimensional -vector model does not belong to the spherically
symmetrical universality class. In the calculations we rely on the
field-theoretical renormalization group approach in different regularization
schemes adjusted by resummation and extended analysis of the series for
renormalization-group functions which are known for the model in high orders of
perturbation theory. The phase diagram of the three-dimensional -vector
model is built marking out domains in the -plane where the model belongs to
a given universality class.Comment: 9 pages, 1 figur
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 ,
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
Critical thermodynamics of three-dimensional chiral model for N > 3
The critical behavior of the three-dimensional -vector chiral model is
studied for arbitrary . The known six-loop renormalization-group (RG)
expansions are resummed using the Borel transformation combined with the
conformal mapping and Pad\'e approximant techniques. Analyzing the fixed point
location and the structure of RG flows, it is found that two marginal values of
exist which separate domains of continuous chiral phase transitions and where such
transitions are first-order. Our calculations yield and
. For the structure of RG flows is identical to
that given by the and 1/N expansions with the chiral fixed point
being a stable node. For the chiral fixed point turns out to be a
focus having no generic relation to the stable fixed point seen at small
and large . In this domain, containing the physical values and , 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.Comment: 12 pages, 3 figure
Critical behavior of two-dimensional frustrated spin models with noncollinear order (vol 64, art no 184408, 2001)
Five-loop epsilon expansion for U(n) x U(m) models: finite-temperature phase transition in light QCD
We 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