One-dimensional models in a solvent

We consider the simple Ising model of M units, each of which can be in either of two states. The configurational PF of such a system is 

We now insert the 1-D system in a solvent w, consisting of N molecules at some temperature T and volume V. Thus in effect we have 3. T, V, N system with one solute inserted at some fixed position and orientation. This solute can be viewed as having many isomers, each characterized by its configuration s. 

Let So be any specific configuration of the 1-D system (this can be chosen as the configuration for which E sq) = 0). Then 

The simplest case of a solvated 1-D system occurs when the coupling work W(s w) is approximately the same for all configurations s. Two examples are shown in Fig. 8.4. In a, the solvent consists of hard-spheres particles and each unit contributes the same excluded volume with respect to the solvent independently of its state (say up or down spin). In this case 1 (81 ) is simply the work required to create a cavity in the solvent to accommodate the 1-D system. The Helmholtz energy levels (8.6.9) are modified by a constant 

In this case IF(cavity) is independent of s therefore, from (8.6.10), we have 

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