Hybrid Monte Carlo algorithm for the double exchange model

Abstract

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 16 3 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. 

Monte Carlo determination of the phase diagram of the double-exchange model

“…We recall that in Ref. 26 it is shown that at J AF ϭ0, T/tϭ0.14 the transition is second order. Although we find a strengthening of this transition when ͉J AF ͉ grows, to confirm that it actually becomes of the first order would require a careful finite-size scaling analysis that is beyond the scope of this work.…”

“…We have extended the previous studies to finite temperatures by using the hybrid Monte Carlo method reported elsewhere, 26 which allows to thermalize 16ϫ16ϫ16 clusters in reasonable computer time. We have studied the model ͑1͒, on the cubic lattice of side L with periodic boundary conditions, using the grand-canonical ensemble ͑4͒.…”

“…In the simulation, we have always used the perfect action formulation, 26 with ϭ0.25, with a sixth degree polynomial. The molecular dynamics parameters have been chosen to ensure an acceptance rate greater than an 80%.…”

“…Our results at finite temperature have been obtained using an efficient hybrid Monte Carlo algorithm, 26 which has been crucial for the exploration of a threedimensional phase diagram. We have found that the competition between the ferromagnetic interaction mediated by the conduction electrons and antiferromagnetic couplings which arise from superexchange effects or from the underlying intra-atomic Hund's coupling lead to the existence of a variety of phases.…”

“…26 We show that the interplay between antiferromagnetic interactions and a three dimensional structure leads to a rich phase diagram, where, in addition to ferro-and antiferromagnetic phases, other ordered phases with cubic symmetry are possible. The model is discussed in the next section.…”