Ashkin-Teller phase transition and multicritical behavior in a classical monomer-dimer model

Abstract

We use Monte Carlo simulations and tensor network methods to study a classical monomer-dimer model on the square lattice with a hole (monomer) fugacity $z$, an aligning dimer-dimer interaction $u$ that favors columnar order, and an attractive dimer-dimer interaction $v$ between two adjacent dimers that lie on the same principal axis of the lattice. The Monte Carlo simulations of finite size systems rely on our grand-canonical generalization of the dimer worm algorithm, while the tensor network computations are based on a uniform matrix product ansatz for the eigenvector of the row-to-row transfer matrix that work directly in the thermodynamic limit. The phase diagram has nematic, columnar order and fluid phases, and a nonzero temperature multicritical point at which all three meet. For any fixed $v/u<\infty$, we argue that this multicritical point continues to be located at a nonzero hole fugacity $z_{\mathrm{mc}}(v/u)>0$; our numerical results confirm this theoretical expectation but find that $z_{\mathrm{mc}}(v/u)\to 0$ very rapidly as $v/u\to \infty$. Our numerical results also confirm the theoretical expectation that the corresponding multicritical behavior is in the universality class of the four-state Potts multicritical point on critical line of the two-dimensional Ashkin-Teller model.

12 pages, 12 figures

References in corpus (6)

• Interacting classical dimers on the square lattice
• Classical dimers with aligning interactions on the square lattice
• Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models
• Correlations and confinement in non-planar two-dimensional dimer models
• Critical Correlations for Short-Range Valence-Bond Wave Functions on the Square Lattice
• Coexistence of long-range and algebraic correlations for short-range valence-bond wave functions in three dimensions

Cited by in corpus (2)

• Phase diagram of a square lattice model of XY Spins with direction-dependent interactions
• CTMRG study of the critical behavior of an interacting-dimer model