Crossed Ising chains: a special decorated two-dimensional Ising model showing a transition to first-order behaviour

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Abstract
A system of crossed Ising chains that can be interpreted as a multiply decorated square Ising lattice is considered and the local spontaneous magnetization which 'hangs through' between the crossing points is discussed. With growing chain distance the coupling constant along the decorated horizontal bonds is allowed to increase such that the critical temperature of the second-order transition remains constant. A narrowing of the critical region with increasing chain distance is observed; in the limit of infinite distance spontaneous magnetization, specific heat and susceptibility exhibit a first-order transition. Thus the model serves as an example for the continuous variation of the character of a phase transition from second to first kind as a function of the 'external parameter' chain distance.

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