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© 2001 Elsevier Science B.V. We acknowledge financial support from grants PB96-0875, AEN97-1680, AEN97-1693, AEN99-0990 (MEC, Spain) and (07N/0045/98) (C. Madrid). V.M.-M. is a MEC fellow. The simulations have been carried out in RTNN computers at Zaragoza and Madrid., The Hybrid Monte Carlo algorithm is adapted to the simulation of a system of classical degrees of freedom coupled to non self-interacting lattices fermions. The diagonalization of the Hamiltonian matrix is avoided by introducing a path-integral formulation of the problem, in d + 1 Euclidean space–time. A perfect action formulation allows to work on the continuum Euclidean time, without need for a Trotter–Suzuki extrapolation. To demonstrate the feasibility of the method we study the Double Exchange Model in three dimensions. The complexity of the algorithm grows only as the system volume, allowing to simulate in lattices as large as 163 on a personal computer. We conclude that the second order paramagnetic–ferromagnetic phase transition of Double Exchange Materials close to half-filling belongs to the Universality Class of the three-dimensional classical Heisenberg model., MEC, Spain, C. Madrid, Spain, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 1998 Elsevier Science B.V. We thank the CICyT (contracts AEN93-0604, AEN96-1634) for partial financial support, especially for the use of dedicated Pentium Pro machines on which we have carried out the simulations. JJRL is granted by EC HMC (ERBFMBICT950429). We also acknowledge to E. Luijten for pointing out the right scaling of the Binder cumulant in the pure case., Using finite-size scaling techniques, we study the critical properties of the site-diluted Ising model in four dimensions. We carry out a high-statistics Monte Carlo simulation for several values of the dilution. The results support the perturbative scenario: there is only the Ising fixed point with large logarithmic scaling corrections. We obtain, using the Perturbative Renormalization Group, functional forms for the scaling of several observables that are in agreement with the numerical data., CICyT, Spain, EC HMC, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 2008 Elsevier B.V. We were partially supported by MEC (Spain) through contract No. FIS-2006-08533-C03-01 and by CAM (Spain) through contract No. CCG07-UCM/ESP-2532., We present Tethered Monte Carlo, a simple, general purpose method of computing the effective potential of the order parameter (Helmholtz free energy). This formalism is based on a new statistical ensemble, closely related to the micromagnetic one, but with an extended configuration space (through Creutz-like demons). Canonical averages for arbitrary values of the external magnetic field are computed without additional simulations. The method is put to work in the two-dimensional Ising model, where the existence of exact results enables us to perform high precision checks. A rather peculiar feature of our implementation, which employs a local Metropolis algorithm, is the total absence, within errors, of critical slowing down for magnetic observables. Indeed, high accuracy results are presented for lattices as large as L = 1024., MEC (Spain), CAM (Spain), Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 2008 Elsevier B.V. We were partially supported by MEC (Spain) through contract No. FIS-2006-08533-C03-01 and by CAM (Spain) through contract No. CCG07-UCM/ESP-2532., We present Tethered Monte Carlo, a simple, general purpose method of computing the effective potential of the order parameter (Helmholtz free energy). This formalism is based on a new statistical ensemble, closely related to the micromagnetic one, but with an extended configuration space (through Creutz-like demons). Canonical averages for arbitrary values of the external magnetic field are computed without additional simulations. The method is put to work in the two-dimensional Ising model, where the existence of exact results enables us to perform high precision checks. A rather peculiar feature of our implementation, which employs a local Metropolis algorithm, is the total absence, within errors, of critical slowing down for magnetic observables. Indeed, high accuracy results are presented for lattices as large as L = 1024., MEC (Spain), Comunidad de Madrid, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 1997 Elsevier Science B.V. International Conference on Lattice Gauge Theory (XIV. 1996. St. Louis/Missouri/EEUU)., We present antiferromagnetism as a mechanism capable of modifying substantially the phase diagram and the critical behaviour of statistical mechanical models. This is particularly relevant in four dimensions, due to the connection between second order transition points and the continuum limit as a quantum field theory. We study three models with an antiferromagnetic interaction: the Ising and the 0(4) Models with a second neighbour negative coupling, and the RP^(2) Model. Different conclusions are obtained depending on the model., Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 1997 Elsevier Science B.V. International Conference on Lattice Gauge Theory (XIV. 1996. Sant Louis/Missouri/EEUU)., We present the results of a Monte Carlo simulation of the antiferromagnetic RP^2 model in three dimensions. With finite-size scaling techniques we accurately measure the critical exponents and compare them with those of O(N) models. We are able to parameterize the corrections-to-scaling. The symmetry properties of the broken phase are also studied., Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 1997 Published by Elsevier Science B.V. We are indebted to A. Sokal for many suggestions. We also thank J.L. Alonso, J.M. Carmona, L.A. Ibort, J.J. Ruiz-Lorenzo and A. Tarancón for discussions. This work has been partially supported by CICyT AEN93-0604-C03-02 and AEN95-1284-E., We study the behavior of the antiferromagnetic RP^2 model in d = 3. The vacuum structure is analyzed in the critical and low temperature regions, paying special attention to the spontaneous symmetry breaking pattern. Near the critical point we observe a full breakdown of the 0(3) symmetry of the action. Several methods for computing critical exponents are compared. We conclude that the most solid determination is obtained using a measure of the correlation length. Corrections-to-scaling are parameterized, yielding a very accurate determination of the critical coupling and a 5% error measure of the related exponent. This is used to estimate the systematic errors due to finite-size effects., CICyT, Spain, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub