First- and second-order phase transitions of infinite-state Potts models in one dimension

The q-state, d-dimensional Potts models exhibit a variety of phase-transition behaviour in the limit d to 1⁺, q to infinity , and l identical to (d-1) in q finite. The regions l<1, 1<l<2, and 2<l are distinguished, respectively, by no transition, second-order transitions (with a new changeover phenomenon at l=ln 4), and first-order transitions. The latter are due to the condensation of effective vacancies. Critical and tricritical exponent values are given.