Low-temperature series for renormalized operators: The ferromagnetic square-lattice Ising model
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: Dynamic critical behavio(u)r of a cluster algorithm for the Ashkin-Teller model
abstract: We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin-Teller model. We find that the Li-Sokal bound on the autocorrelation time (τint,ɛ ≥ const × CH) holds along the self-dual curve of the symmetric Ashkin-Teller model, but this bound is apparently not sharp. The ratio τint, ɛ /CH appears to tend to infinity either as a logarithm or as a small power (0.05 ≲ p ≲ 0.12).

title: Dynamic critical behavior of a Swendsen-Wang-Type algorithm for the Ashkin-Teller model
abstract: We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin-Teller model. We find that the Li-Sokal bound on the autocorrelation time (τint.δ≥ const xCH) holds along the self-dual curve of the symmetric Ashkin-Teller model, and is almost, but not quite sharp. The ratio τint.δ/CH appears to tend to infinity either as a logarithm or as a small power (0.05≲p≲0.12). In an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time.

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: Computing the couplings of Ising systems from Schwinger-Dyson equations
abstract: We study the problem of determining the couplings of Ising systems in terms of expectation values. We find that all previously known methods can be based on Schwinger-Dyson equations. Indeed, new methods can be derived with relative advantages with respect to all of them. Application for the renormalization group flow of the Ising model on a square lattice is presented.

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: 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.