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

초록

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<∞, we argue that this multicritical point continues to be located at a nonzero hole fugacity zmc(v/u)>0; our numerical results confirm this theoretical expectation but find that zmc(v/u)→0 very rapidly as v/u→∞. 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. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.