# Columnar order and Ashkin-Teller criticality in mixtures of hard-squares and dimers

### Kabir Ramola 1 Kedar Damle 2 Deepak Dhar 2

#### Physical Review Letters, American Physical Society, 2015, 114, pp.190601

Particles with only hard-core interactions can exhibit interesting high-density phases. The cases of particles in the shape of $2\times2$ squares, and $2\times 1$ dimers on a square lattice have been studied for a long time. Here, we study the interesting and more general problem of a mixture of such dimers and squares. In the fully-packed limit of no vacancies, increasing the fraction of squares enhances the power-law columnar (stripe) order present in the pure dimer limit and eventually leads to a Kosterlitz-Thouless-type (KT) phase transition to a square-rich phase with long-range columnar order. With vacancies allowed, the entire phase boundary between this columnar ordered phase and the low-density fluid phase has continuously varying exponents and is in the Ashkin-Teller universality class. These results, which we confirm by Monte-Carlo simulations, make explicit the Ashkin-Teller nature of the density-driven transition in the $2\times 2$ hard-square gas.

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 2. Tata Institute of Fundamental Research