Critical temperature and density of spin flips in the anisotropic random-field Ising model

We present analytical results for the strongly anisotropic random-field Ising model, consisting of weakly interacting spin chains. We combine the mean-field treatment of interchain interactions with an analytical calculation of the average chain free energy ("chain mean-field'' approach). The free energy is found using a mapping on a Brownian motion model. We calculate the order parameter and give expressions for the critical random magnetic-field strength below which the ground state exhibits long-range order and for the critical temperature as a function of the random magnetic-field strength. In the limit of vanishing interchain interactions, we obtain corrections to the zero-temperature estimate by Imry and hla [Phys. Rev. Lett. 35, 1399 (1975)] of the ground-state density of domain walls (spin flips) in the one-dimensional random-field Ising model. One of the problems to which our model has direct relevance is the lattice dimerization in disordered quasi-one-dimensional Peierls materials, such as the conjugated polymer trans-polyacetylene. [S0163-1829(98)02129-8].