402 research outputs found

### Two-Dimensional Heisenberg Model with Nonlinear Interactions

We investigate a two-dimensional classical $N$-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 $p>p_c$ and no finite-temperature
phase transitions for $p p_c$, both phases have short-range
order, the correlation length showing a finite discontinuity at the transition.
For $p=p_c$, 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

### Discrete non-Abelian groups and asymptotically free models

We consider a two-dimensional $\sigma$-model with discrete
icosahedral/dodecahedral symmetry. Using the perturbative renormalization
group, we argue that this model has a different continuum limit with respect to
the O(3) $\sigma$ model. Such an argument is confirmed by a high-precision
numerical simulation.Comment: 5 pages including 6 postscript figures. Talk given at HEP01 in
Budapest, Hungary, in July 200

### 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

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