Related papers: Sampling Colourings of the Triangular Lattice
We give tight upper and lower bounds on the internal energy per particle in the antiferromagnetic $q$-state Potts model on $4$-regular graphs, for $q\ge 5$. This proves the first case of a conjecture of the author, Perkins, Jenssen, and…
In this work, we consider a number of problems defined on the triangular lattice with $n$ rows, which we will denote as $T_n$. Define a \textit{proper coloring} to be an assignment of colors to the points of $T_n$ such that no three points…
A strong edge-colouring of a graph is a proper edge-colouring where each colour class induces a matching. It is known that every planar graph with maximum degree $\Delta$ has a strong edge-colouring with at most $4\Delta+4$ colours. We show…
We propose and study a model with glassy behavior. The state space of the model is given by all triangulations of a sphere with $n$ nodes, half of which are red and half are blue. Red nodes want to have 5 neighbors while blue ones want 7.…
Felsner, Hurtado, Noy and Streinu (2000) conjectured that arrangement graphs of simple great-circle arrangements have chromatic number at most $3$. Motivated by this conjecture, we study the colorability of arrangement graphs for different…
Folding of the triangular lattice in a discrete three-dimensional space is investigated numerically. Such ``discrete folding'' has come under through theoretical investigation, since Bowick and co-worker introduced it as a simplified model…
A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest neighbor spin couplings and then evaluating the Pfaffian of the…
The relationship between the coincidence indices of a lattice $\Gamma_1$ and a sublattice $\Gamma_2$ of $\Gamma_1$ is examined via the colouring of $\Gamma_1$ that is obtained by assigning a unique colour to each coset of $\Gamma_2$. In…
We show for a broad class of counting problems, correlation decay (strong spatial mixing) implies FPTAS on planar graphs. The framework for the counting problems considered by us is the Holant problems with arbitrary constant-size domain…
Generative models have advanced significantly in sampling material systems with continuous variables, such as atomistic structures. However, their application to discrete variables, like atom types or spin states, remains underexplored. In…
We investigate the trion formation and the effective trionic properties in the attractive Hubbard model with three fermionic colors using exact diagonalization. The crossover to the trionic regime with colorless compound fermions upon…
We show that a multicolor modulation of the depth of an optical lattice allows for a flexible independent control of correlated hopping, occupation-dependent gauge fields, effective on-site interactions without Feshbach resonances, and…
We construct a model of short-range interacting Ising spins on a translationally invariant two-dimensional lattice that mimics a reversible circuit that multiplies or factorizes integers, depending on the choice of boundary conditions. We…
We measure the two-point angular correlation function of a sample of 4,289,223 galaxies with r < 19.4 mag from the Sloan Digital Sky Survey as a function of photometric redshift, absolute magnitude and colour down to M_r - 5log h = -14 mag.…
The random-cluster model has been widely studied as a unifying framework for random graphs, spin systems and electrical networks, but its dynamics have so far largely resisted analysis. In this paper we analyze the Glauber dynamics of the…
Motivated by a recent conjecture of the first author, we prove that every properly coloured triangle-free graph of chromatic number $\chi$ contains a rainbow independent set of size $\lceil\frac12\chi\rceil$. This is sharp up to a factor…
A particular discrete rhombohedral lattice consisting of four symmetrically interlaced cuboctahedral point lattices is described that is interesting because of the high degree of symmetry it exhibits. The four constituent cuboctahedral…
Spin systems are fundamental models of statistical physics that provide insight into collective behavior across scientific domains. Their interest to computer science stems in part from the deep connection between the phase transitions they…
We study a one-dimensional two-component Fermi gas in a harmonic trapping potential using finite temperature lattice quantum Monte Carlo methods. We are able to compute observables in the canonical ensemble via an efficient projective…
Motivated by the spate of recent experimental and theoretical interest in Mott insulating S=1 triangular lattice magnets, we consider a model S=1 Hamiltonian on a triangular lattice interacting with rotationally symmetric biquadratic…