Related papers: The random cluster model and new summation and int…
We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $\rho$ and inverse temperature $\beta$ differs from the one of the…
Robustly determining the optimal number of clusters in a data set is an essential factor in a wide range of applications. Cluster enumeration becomes challenging when the true underlying structure in the observed data is corrupted by…
We investigate the geometry of a typical spin cluster in random triangulations sampled with a probability proportional to the energy of an Ising configuration on their vertices, both in the finite and infinite volume settings. This model is…
For a family of random-cluster models with cluster weights $q\geq 1$, we prove that the probability that $0$ is connected to $x$ is asymptotically equal to $\tfrac{1}{q}\chi(\beta)^{2}\beta J_{0,x}$. The method developed in this article can…
We divide the free energy near the critical point into two parts. One is the regular part, the other is the singular part. The singular part is assumed to be a concrete possible form. The singular part in this form is different from Widom…
We investigate the critical properties of the spin-3/2 Blume-Capel model in two dimensions on a random lattice with quenched connectivity disorder. The disordered system is simulated by applying the cluster hybrid Monte Carlo update…
We prove an upper bound for the free energy (per unit volume) of the dilute Bose gas in the thermodynamic limit, showing that the free energy at density $\rho$ and inverse temperature $\beta$ differs from that of the non-interacting system…
We present cluster Monte Carlo algorithms for the $XYZ$ quantum spin models. In the special case of $S=1/2$, the new algorithm can be viewed as a cluster algorithm for the 8-vertex model. As an example, we study the $S=1/2$ $XY$ model in…
The free energy, or equivalently the ground state energy in finite volume, may be calculated from forward scattering amplitudes using a formula due to Dashen, Ma, and Bernstein. However a naive treatment leads to singularities when…
We consider the free energy of a class of spin glass models with $ p$-spin interactions in a transverse magnetic field. As $ p \to \infty $, the infinite system-size free energy is proven to converge to that of the quantum random energy…
We present a large $q$ expansion of the 2d $q$-states Potts model free energies up to order 9 in $1/\sqrt{q}$. Its analysis leads us to an ansatz which, in the first-order region, incorporates properties inferred from the known critical…
We present a new way of probing the universality class of the site-diluted two-dimensional Ising model. We analyse Monte Carlo data for the magnetic susceptibility, introducing a new fitting procedure in the critical region applicable even…
We investigate the nucleation dynamics of the three-dimensional random field Ising model (RFIM) under an external field. We use umbrella sampling to compute the free-energy cost of a critical nucleus, and use forward flux sampling for the…
We develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum -- and, in particular, classical -- interactions. Our approach is based on the use of ``decoupling parameters", advocated by Park [34], which…
We show analytically that the perturbative expansion for the free energy of the zero dimensional (quenched) disordered Ising model is Borel-summable in a certain range of parameters, provided that the summation is carried out in two steps:…
We develop a method to calculate the bipartite entanglement entropy of quantum models, in the thermodynamic limit, using a Numerical Linked Cluster Expansion (NLCE) involving only rectangular clusters. It is based on exact diagonalization…
We develop an ansatz for expressing the free energy of the two dimensional $q$-states Potts model for $q > 4$ near its first order phase transition point. We notice that for the moderate values of $ q \lesssim 15 $, the energy profile at…
We study the free energy for pure and mixed spherical $p$-spin models with i.i.d.\ disorder. In the mixed case, each $p$-interaction layer is assumed either to have regularly varying tails with exponent $\alpha_p$ or to satisfy a finite…
We generalize the small scale dynamics of the universe by taking into account models with an equation of state which evolves with time, and provide a complete formulation of the cluster virialization attempting to address the nonlinear…
Monte-Carlo simulations on a variety of 2d percolating systems at criticality suggest that the excess number of clusters in finite systems over the bulk value of nc is a universal quantity, dependent upon the system shape but independent of…