Ladder Ising Spin Configurations II. Magnetic Properties

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In this paper we consider ladders with two, three, and four coupled Ising spin chains, characterized by interchain and intrachain couplings, to study in detail their magnetic behaviour for different ratios of the interaction constants and different values of magnetic field, by using a transfer matrix method and a complex algorithm, realizing the diagonalization and the differentiation. We have proposed a combined algorithm to realize also the generation of the elements of the transfer matrix for more complicated ladder configurations. The problem of Ising ladders is straightforward with a crossover between a 2D high-temperature region and a ID low-temperature region when the 2D correlation length equals the width. To emphasize the fact that there is no finite magnetization in absence of the magnetic field, we study also analytically this case for the ladder with two coupled Ising chains. In presence of the magnetic field, for very weak magnetic fields (of the order 10-8, in reduced units) the magnetization goes from the value one to the value zero in a narrow interval of nonzero temperatures, where also the susceptibility exhibits a very high peak. This narrow interval, increasing the number of chains, is displaced towards higher temperatures. Also, in the case of interchain antiferromagnetic couplings, the formation of interchain spin pairs becomes clear.

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