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Monte Carlo simulations, using the PERM algorithm, of interacting self-avoiding walks (ISAW) and interacting self-avoiding trails (ISAT) in five dimensions are presented which locate the collapse phase transition in those models. It is argued that the appearance of a transition (at least) as strong as a pseudo-first-order transition occurs in both models. The values of various theoretically conjectured dimension-dependent exponents are shown to be consistent with the data obtained. Indeed the first-order nature of the transition is even stronger in five dimensions than four. The agreement with the theory is better for ISAW than ISAT and it cannot be ruled out that ISAT have a true first-order transition in dimension five. This latter difference would be intriguing if true. On the other hand, since simulations are more difficult for ISAT than ISAW at this transition in high dimensions, any discrepancy may well be due to the inability of the simulations to reach the true asymptotic regime.
We numerically investigate the influence of self-attraction on the critical behaviour of a polymer in two dimensions, by means of an analysis of finite-size results of transfer-matrix calculations. The transfer matrix is constructed on the basis of t
We present a Monte Carlo method for the direct evaluation of the difference between the free energies of two crystal structures. The method is built on a lattice-switch transformation that maps a configuration of one structure onto a candidate config
Accelerated algorithms for simulating the morphological evolution of strained heteroeptiaxy based on a ball and spring lattice model in three dimensions are explained. We derive exact Greens function formalisms for boundary values in the associated l
We show how the directed-loop Monte Carlo algorithm can be applied to study vertex models. The algorithm is employed to calculate the arrow polarization in the six-vertex model with the domain wall boundary conditions (DWBC). The model exhibits spati
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