Phase transitions in systems of lattice-dimers with nearest neighbor interactions

A dense system of dimers on hypercubic lattices is studied with Monte Carlo simulation, where dimers are displaced concomitantly in loops. A mixture of A- and B-dimers with an attractive interaction of strength unity between identical nearest neighbors, where the number of A- or B-dimers can fluctuate but not their sum, undergoes an Ising-type demixing transition of second order when changing the temperature. The transition temperatures are Tc ∾ 1.71 and Tc ∾ 3.91 on a square and cubic lattice, respectively. A system of co-dimers, where a co-dimer consists of an A- and a B-subunit, with an attractive interaction between identical nearest neighbors, undergoes a microphase separation, where the dimers orient into a lattice direction. In two dimensions the transition at Tc ∾ 0.831 is of second order and the critical exponents ν ∾ 0.67 and β ∾ 0.11, determined by finite size scaling, do not belong to the Ising class. In three dimensions the transition at Tc ∾ 1.15 is first order. Random error estimates are better than 1% for the critical temperatures, about 2–4% for ν and about 10% for β. However, no estimation of possible systematic errors due to corrections to finite size scaling has been attempted.