Properties of a random bond Ising chain in a magnetic field

Abstract

The Ising chain with random bonds in a magnetic field $\mathcal{H}=-\Sigma i^{}{J}_i{\sigma }_i{\sigma }_{i+1\mathrm{}}-h\Sigma i^{}{\sigma }_i$, where $J_i=\pm 1$ at random, and $\Sigma i^{}{J}_i=0\mathrm{}$, represents a model of a magnetic glass, or of heteropolymer melting. Calculations of the thermodynamic properties of the chain as a function of field strength and temperature have been performed by Monte Carlo techniques. These results are compared with perturbation calculations for small and large values of $\frac{h}{T}$. The Monte Carlo results show, in agreement with the perturbation calculations, that the field-induced magnetization is generally smaller for the random bond model than for a chain of noninteracting spins. As $T\to 0$ the magnetization approaches the result for noninteracting spins.