Walks with up to two monomers per site on the Bethe lattice: Interpolation between models with immediate reversals allowed and immediate reversals forbidden

Abstract

We generalize earlier calculations of the RA (immediate reversals allowed) and RF (immediate reversals forbidden) model with multiple monomers per site, including a parameter in the model, so that both cases studied before are particular cases of the model considered here. Also, we calculate the bulk free energy of the model using Gujrati’s prescription, which leads to corrections in the localization of coexistence lines and qualitative changes in the phase diagram of the model. Thus, this calculation provides an example in which the use of the method of iterating recursion relations starting with natural initial conditions to locate coexistence loci is not trustworthy and may lead to qualitatively different results. A continuous collapse transition appears in all cases as a tricritical point.