771 research outputs found
Large-N_f chiral transition in the Yukawa model
We investigate the finite-temperature behavior of the Yukawa model in which
fermions are coupled with a scalar field in the limit . Close to the chiral transition the model shows a crossover between
mean-field behavior (observed for ) and Ising behavior (observed
for any finite ). We show that this crossover is universal and related to
that observed in the weakly-coupled theory. It corresponds to the
renormalization-group flow from the unstable Gaussian fixed point to the stable
Ising fixed point. This equivalence allows us to use results obtained in field
theory and in medium-range spin models to compute Yukawa correlation functions
in the crossover regime
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
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
Randomly dilute spin models: a six-loop field-theoretic study
We consider the Ginzburg-Landau MN-model that describes M N-vector cubic
models with O(M)-symmetric couplings. We compute the renormalization-group
functions to six-loop order in d=3. We focus on the limit N -> 0 which
describes the critical behaviour of an M-vector model in the presence of weak
quenched disorder. We perform a detailed analysis of the perturbative series
for the random Ising model (M=1). We obtain for the critical exponents: gamma =
1.330(17), nu = 0.678(10), eta = 0.030(3), alpha=-0.034(30), beta = 0.349(5),
omega = 0.25(10). For M > 1 we show that the O(M) fixed point is stable, in
agreement with general non-perturbative arguments, and that no random fixed
point exists.Comment: 29 pages, RevTe
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
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