Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem
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: 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: 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: "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: Dynamic critical behavior of the Swendsen-Wang algorithm: The two-dimensional three-state Potts model revisited
abstract: We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Sweden-Wang algorithm for the two-dimensional three-state Potts model. We find that the Li-Sokal bound (τint.δ⩾const×Cn) is almost but not quite sharp. The ratio τint.δ/Cn seems to diverge either as a small power (≈0.08) or as a logarithm.

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.