Properties of a random bond Ising chain in a magnetic field

Abstract

The Ising chain with random bonds in a magnetic field $\mathcal{H}=\ensuremath{-}\ensuremath{\Sigma}{i}^{}{J}_{i}{\ensuremath{\sigma}}_{i}{\ensuremath{\sigma}}_{i+1}\ensuremath{-}h\ensuremath{\Sigma}{i}^{}{\ensuremath{\sigma}}_{i}$, where ${J}_{i}=\ifmmode\pm\else\textpm\fi{}1$ at random, and $\ensuremath{\Sigma}{i}^{}{J}_{i}=0$, 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 $T\ensuremath{\rightarrow}0$ the magnetization approaches the result for noninteracting spins.