A toy model for the pseudogap state of cuprates

A toy model is developed to capture "dance of pre-formed pairs" in the pseudogap state of high temperature cuprate superconductors. The model is a crude description of a hypothetical situation in which spin-driven spatial organization of the pre-formed pairs is analyzed. Within a mean-field theory (a slight generalization of Bragg-Williams theory) we examined the behaviour of heat capacity and an "order parameter" which captures the short range correlations between the pre-formed pairs. Below a transition temperature these short range correlations enhance and leads to a long range order (spin-density wave). This is examined through the breakdown of statistical independence.