Ising models on the pentagon lattice

We solve inhomogeneous Ising models on the pentagon lattice using the transfer matrix formalism. As two special cases we study the ferromagnetic and the fully frustrated antiferromagnetic model on this lattice. The ferromagnet shows a phase transition at someT _c>0 with the usual Ising behaviour. In the frustrated case no transition occurs at any temperature due to frustration. Frustration also causes a nonvanishing rest entropy. We also calculate the spin-spin-correlation for large distance in both cases. In the ferromagnetic model we thus get the magnetization and the expected algebraic (exponential) decay of the correlations at (above)T _c. The correlations of the frustrated model decay exponentially for all temperatures, includingT=0, indicating that evenT=0 belongs to the disordered high temperature phase. Superimposed to the exponential decay the correlation shows an interesting oscillatory behaviour with temperature dependent wave number, i.e. an incommensurate structure.Work performed within the research program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln