405 research outputs found

    Two-Dimensional Heisenberg Model with Nonlinear Interactions

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

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    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

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    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

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    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

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    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

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    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

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    We review results concerning the critical behavior of spin systems at equilibrium. We consider the Ising and the general O(NN)-symmetric universality classes, including the N0N\to 0 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 NN-component systems with cubic anisotropy, O(NN)-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 β\beta-functions. Finally, we consider a Hamiltonian with symmetry O(n1)O(n2)O(n_1)\oplus O(n_2) that is relevant for the description of multicritical phenomena.Comment: 151 pages. Extended and updated version. To be published in Physics Report
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