A Generalized Kac Model as a Dynamical System*
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چکیده
Here cp denotes the phase of the complex interaction parameter k, and crt= ± 1 stands for the spin variable at site i. The interaction energy between two sites at distance x decays exponentially with x but now with an oscillating amplitude of wavelength In/cp. This oscillation mimics the effect of the indirect exchange interaction between spins mediated by electrons that leads in realistic models to RKKY type interaction with an algebraic decay [3]. The generalized Kac model, (1, 2), has been introduced in [2], Here we pres ent some results concerning the dependence on the phase (p not published before and discuss them in a broader context. The basic observation of our approach is that ther mal properties of the Kac chains (such as free energy, magnetization, heat capacity etc.) can be obtained from a simple functional representation of the transfer matrix [4], For the generalized model the transfer ma trix if can be represented in the space of holomorfic
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تاریخ انتشار 2013