arXiv subjects

G. Rakala

Publications and source records attributed to G. Rakala.

3 recordsLinked to original sources

arXiv2022

Phases of the hard-plate lattice gas on a three-dimensional cubic lattice

We study the phase diagram of a system of $2\times 2\times 1$ hard plates on the three dimensional cubic lattice, {\em i.e.} a lattice gas of plates that each cover an elementary plaquette of the cubic lattice and occupy its four vertices, with the constraint that no two plates occupy the same site of the cubic lattice. We focus on the isotropic system, with equal fugacities for the three orientations of plates. We show, using grand canonical Monte Carlo simulations, that the system undergoes two density-driven phase transitions with increasing density of plates: the first from a disordered fluid to a layered phase, and the second from the layered phase to a sublattice-ordered phase. In the layered phase, the system breaks up into disjoint slabs of thickness two along one spontaneously chosen cartesian direction. Plates with normals perpendicular to this layering direction are preferentially contained entirely within these slabs, while plates straddling two successive slabs have a lower density. Additionally the symmetry between the three types of plates is spontaneously broken, as plates with normal along the layering direction have a lower density than the other two types of plates. Intriguingly, the occupied slabs exhibit two-dimensional power-law columnar order even in the presence of a nonzero density of vacancies. In contrast, inter-slab correlations of the two-dimensional columnar order parameter decay exponentially with the separation between the slabs. In the sublattice-ordered phase, there is two-fold ($Z_2$) breaking of lattice translation symmetry along all three cartesian directions. We present numerical evidence that the disordered to layered transition is continuous and consistent with the three-dimensional $O(3)$ universality class, while the layered to sublattice transition is first-order in nature.

cond-mat.stat-mech↗

arXiv2022

Spontaneous layering and power-law order in the three-dimensional fully-packed hard-plate lattice gas

We obtain the phase diagram of fully-packed hard plates on a cubic lattice. Each plate covers an elementary plaquette of the cubic lattice and occupies its four vertices, with each vertex of the cubic lattice occupied by exactly one such plate. We consider the general case with fugacities $s_μ$ for `$μ$ plates', whose normal is the $μ$ direction ($μ= x,y,z$). At and close to the isotropic point, we find, consistent with previous work, a phase with long-range sublattice order. When two of the fugacities $s_{\rm μ_1}$ and $s_{μ_2}$ are comparable, and the third fugacity $s_{μ_{3}}$ is much smaller, we find a spontaneously-layered phase. In this phase, the system breaks up into disjoint slabs of width two stacked along the $μ_3$ axis. $μ_1$ and $μ_2$ plates are preferentially contained entirely within these slabs, while plates straddling two successive slabs have a lower density. In the opposite limit, with $μ_3 \gg μ_1 \sim μ_2$, we find a phase with long-range columnar order, corresponding to simultaneous $Z_2$ symmetry breaking of lattice translation symmetry in directions $μ_1$ and $μ_2$. The spontaneously-layered phases display critical behaviour, with power-law decay of correlations in the $μ_1$ and $μ_2$ directions when the slabs are stacked in the $μ_3$ direction, and represent examples of `floating phases' discussed earlier in the context of coupled Luttinger liquids and quasi-two-dimensional classical systems. We ascribe this remarkable behaviour to the constrained motion of defects in this phase, and develop a coarse-grained effective field theoretical understanding of the stability of power-law order in this unusual three-dimensional floating phase.

cond-mat.stat-mech↗

arXiv2021

Melting of three-sublattice order in triangular lattice Ising antiferromagnets: Power-law order, $Z_6$ parafermionic multicriticality, and weakly first order transitions

The nature of the thermal melting process by which triangular-lattice Ising antiferromagnets lose their low-temperature ferrimagnetic three-sublattice order depends on the range of the interactions: It changes character when second and third neighbour ferromagnetic interactions become comparable to the nearest-neighbour antiferromagnetic coupling. We present a detailed numerical characterization of the corresponding threshold at which two-step melting of three-sublattice order gives way to a direct first-order transition at which this order is lost. The multicritical behaviour at this threshold is argued to be in the universality class of the $Z_6$ parafermion conformal field theory with central charge $c=5/4$. The presence of this multicritical threshold influences the melting behaviour and long-wavelength properties over a fairly large range of parameters, and at temperatures that are of the same order as the exchange interactions. It is therefore of potential experimental relevance in the context of easy-axis triangular lattice antiferromagnets that display such low temperature ordering.

cond-mat.stat-mech↗