405 research outputs found
Two-Dimensional Heisenberg Model with Nonlinear Interactions
We investigate a two-dimensional classical -vector model with a nonlinear
interaction (1 + \bsigma_i\cdot \bsigma_j)^p in the large-N limit. As
observed for N=3 by Bl\"ote {\em et al.} [Phys. Rev. Lett. {\bf 88}, 047203
(2002)], we find a first-order transition for and no finite-temperature
phase transitions for , both phases have short-range
order, the correlation length showing a finite discontinuity at the transition.
For , there is a peculiar transition, where the spin-spin correlation
length is finite while the energy-energy correlation length diverges.Comment: 7 pages, 2 figures in a uufile. Discussion of the theory for p = p_c
revised and enlarge
Renormalization-group flow and asymptotic behaviors at the Berezinskii-Kosterlitz-Thouless transitions
We investigate the general features of the renormalization-group flow at the
Berezinskii-Kosterlitz-Thouless (BKT) transition, providing a thorough
quantitative description of the asymptotc critical behavior, including the
multiplicative and subleading logarithmic corrections. For this purpose, we
consider the RG flow of the sine-Gordon model around the renormalizable point
which describes the BKT transition. We reduce the corresponding beta-functions
to a universal canonical form, valid to all perturbative orders. Then, we
determine the asymptotic solutions of the RG equations in various critical
regimes: the infinite-volume critical behavior in the disordered phase, the
finite-size scaling limit for homogeneous systems of finite size, and the
trap-size scaling limit occurring in 2D bosonic particle systems trapped by an
external space-dependent potential.Comment: 16 pages, refs adde
Critical mass renormalization in renormalized phi4 theories in two and three dimensions
We consider the O(N)-symmetric phi4 theory in two and three dimensions and
determine the nonperturbative mass renormalization needed to obtain the phi4
continuum theory. The required nonperturbative information is obtained by
resumming high-order perturbative series in the massive renormalization scheme,
taking into account their Borel summability and the known large-order behavior
of the coefficients. The results are in good agreement with those obtained in
lattice calculations.Comment: 4 page
Three-dimensional ferromagnetic CP(N-1) models
We investigate the critical behavior of three-dimensional ferromagnetic
CP(N-1) models, which are characterized by a global U(N) and a local U(1)
symmetry. We perform numerical simulations of a lattice model for N=2, 3, and
4. For N=2 we find a critical transition in the Heisenberg O(3) universality
class, while for N=3 and 4 the system undergoes a first-order transition. For
N=3 the transition is very weak and a clear signature of its discontinuous
nature is only observed for sizes L>50. We also determine the critical behavior
for a large class of lattice Hamiltonians in the large-N limit. The results
confirm the existence of a stable large-N CP(N-1) fixed point. However, this
evidence contradicts the standard picture obtained in the
Landau-Ginzburg-Wilson (LGW) framework using a gauge-invariant order parameter:
the presence of a cubic term in the effective LGW field theory for any N>2
would usually be taken as an indication that these models generically undergo
first-order transitions.Comment: 14 page
Interacting N-vector order parameters with O(N) symmetry
We consider the critical behavior of the most general system of two N-vector
order parameters that is O(N) invariant. We show that it may a have a
multicritical transition with enlarged symmetry controlled by the chiral
O(2)xO(N) fixed point. For N=2, 3, 4, if the system is also invariant under the
exchange of the two order parameters and under independent parity
transformations, one may observe a critical transition controlled by a fixed
point belonging to the mn model. Also in this case there is a symmetry
enlargement at the transition, the symmetry being [SO(N)+SO(N)]xC_2, where C_2
is the symmetry group of the square.Comment: 14 page
Operator Product Expansion on the Lattice: a Numerical Test in the Two-Dimensional Non-Linear Sigma-Model
We consider the short-distance behaviour of the product of the Noether O(N)
currents in the lattice nonlinear sigma-model. We compare the numerical results
with the predictions of the operator product expansion, using one-loop
perturbative renormalization-group improved Wilson coefficients. We find that,
even on quite small lattices (m a \approx 1/6), the perturbative operator
product expansion describes that data with an error of 5-10% in a large window
2a \ltapprox x \ltapprox m^{-1}. We present a detailed discussion of the
possible systematic errors.Comment: 53 pages, 11 figures (26 eps files
Critical Phenomena and Renormalization-Group Theory
We review results concerning the critical behavior of spin systems at
equilibrium. We consider the Ising and the general O()-symmetric
universality classes, including the limit that describes the critical
behavior of self-avoiding walks. For each of them, we review the estimates of
the critical exponents, of the equation of state, of several amplitude ratios,
and of the two-point function of the order parameter. We report results in
three and two dimensions. We discuss the crossover phenomena that are observed
in this class of systems. In particular, we review the field-theoretical and
numerical studies of systems with medium-range interactions. Moreover, we
consider several examples of magnetic and structural phase transitions, which
are described by more complex Landau-Ginzburg-Wilson Hamiltonians, such as
-component systems with cubic anisotropy, O()-symmetric systems in the
presence of quenched disorder, frustrated spin systems with noncollinear or
canted order, and finally, a class of systems described by the tetragonal
Landau-Ginzburg-Wilson Hamiltonian with three quartic couplings. The results
for the tetragonal Hamiltonian are original, in particular we present the
six-loop perturbative series for the -functions. Finally, we consider a
Hamiltonian with symmetry that is relevant for the
description of multicritical phenomena.Comment: 151 pages. Extended and updated version. To be published in Physics
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