Dynamic critical behavior of cluster algorithms for 2D Ashkin-Teller and Potts models
We study the dynamic critical behavior of two algorithms: the Swendsen-Wang algorithm for the two-dimensional Potts model with q=2,3,4 and a Swendsen-Wang-type algorithm for the two-dimensional symmetric Ashkin-Teller model on the self-dual curve. We find that the Li--Sokal bound on the autocorrelation time \tau_{{\rm int},{\cal E}} \geq const \times C_H is almost, but not quite sharp. The ratio \tau_{{\rm int},{\cal E}}/C_H appears to tend to infinity either as a logarithm or as a small power (0.05 \ltapprox p \ltapprox 0.12). We also show that the exponential autocorrelation time \tau_{{\rm exp},{\cal E}} is proportional to the integrated autocorrelation time \tau_{{\rm int},{\cal E}}.

title: "The Ising model on spherical lattices: dimer versus Monte Carlo approach"
abstract: We study, using dimer and Monte Carlo approaches, the critical properties and finite size effects of the Ising model on honeycomb lattices folded on the tetrahedron. We show that the main critical exponents are not affected by the presence of conical singularities. The finite size scaling of the position of the maxima of the specific heat does not match, however, with the scaling of the correlation length, and the thermodynamic limit is attained faster on the spherical surface than in corresponding lattices on the torus.  imtjg64@cc.csic.es e-mail: duncan@vm1.sdi.uam.es

title: Phase diagram of the chromatic polynomial on a torus
abstract: We study the zero-temperature partition function of the Potts antiferromagnet (i.e., the chromatic polynomial) on a torus using a transfer-matrix approach. We consider square- and triangular-lattice strips with fixed width L, arbitrary length N, and fully periodic boundary conditions. On the mathematical side, we obtain exact expressions for the chromatic polynomial of widths L = 5, 6, 7 for the square and triangular lattices. On the physical side, we obtain the exact phase diagrams for these strips of width L and infinite length, and from these results we extract useful information about the infinite-volume phase diagram of this model: in particular, the number and position of the different phases.

title: Low-temperature series for renormalized operators: The ferromagnetic square-lattice Ising model
abstract: A method for computing low-temperature series for renormalized operators in the two-dimensional Ising model is proposed. These series are applied to the study of the properties of the truncated renormalized Hamiltonians when we start at very low temperature and zero field. The truncated Hamiltonians for majority rule, Kadanoff transformation, and decimation for 2×2 blocks depend on the how we approach the first-order phase-transition line. The renormalization group transformations are multivalued and discontinuous at this first-order transition line when restricted to some finite-dimensional interaction space.

title: Exact finite-size-scaling corrections to the critical two-dimensional Ising model on a torus: II. Triangular and hexagonal lattices
abstract: We compute the finite-size corrections to the free energy, internal energy and specific heat of the critical two-dimensional spin-1/2 Ising model on triangular and hexagonal lattices wrapped on a torus. We find the general form of the finite-size corrections to these quantities, as well as explicit formulae for the first coefficients of each expansion. We analyse the implications of these findings for the renormalization-group description of the model.

title: Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem
abstract: We prove that theq-state Potts antiferromagnet on a lattice of maximum coordination numberr exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) wheneverq>2r. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay forq≥7), triangular lattice (q≥11), hexagonal lattice (q≥4), and Kagomé lattice (q≥6). The proofs are based on the Dobrushin uniqueness theorem.

title: Adiabatic regularization and particle creation for spin one-half fields
abstract: The extension of the adiabatic regularization method to spin-$1/2$ fields requires a self-consistent adiabatic expansion of the field modes. We provide here the details of such expansion, which differs from the WKB ansatz that works well for scalars, to firmly establish the generalization of the adiabatic renormalization scheme to spin-$1/2$ fields. We focus on the computation of particle production in de Sitter spacetime and obtain an analytic expression of the renormalized stress-energy tensor for Dirac fermions.