Statistical mechanics of Ising chains in random magnetic fields

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Abstract
For a model of heteropolymer ’’melting,’’ we study an Ising model where the field on each spin can randomly take one of the two values H±h. Several numerical methods for the calculation of the free energy and its derivatives are developed, making use of a transfer matrix representation of the partition function and mathematical theorems on random matrices due to Bellman. Monte Carlo computations due to Landau and Blume on the model with H=0 are extended to the case H≠0 and compared with the above results. The efficiency of our other numerical methods is found to be better by more than one order of magnitude than the Monte Carlo technique, as far as the calculation of energy, magnetization, etc. is concerned. But the Monte Carlo technique also yields time‐dependent correlation functions and information on the concentrations of clusters of subsequent up (or down) spins. These quantities are compared to the corresponding ones of the ordinary Glauber model. We find that these quantities can fairly be approximated by the Glauber ones, but using a suitably renormalized correlation length. These results support the ’’coarse‐graining approximation’’ proposed for the statistical mechanics of heteropolymers