Hybrid Monte Carlo algorithm for the double exchange model

© 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
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