We determine the backbone exponent X(b) of several critical and tricritical q-state Potts models in two dimensions. The critical systems include the bond percolation, the Ising, the q=2-sqrt[3], 3, and 4 state Potts, and the Baxter-Wu model, and the tricritical ones include the q=1 Potts model and the Blume-Capel model. For this purpose, we formulate several efficient Monte Carlo methods and sa...

In this survey, we give a friendly introduction from a graph theory perspective to the q-state Potts model, an important statistical mechanics tool for analyzing complex systems in which nearest neighbor interactions determine the aggregate behavior of the system. We present the surprising equivalence of the Potts model partition function and one of the most renowned graph invariants, the Tutte...

We investigate geometric properties of the general q-state Potts model in two dimensions, and define geometric clusters as sets of lattice sites in the same Potts state, connected by nearest-neighbor bonds with variable probability p. We find that, besides the random-cluster fixed point, both the critical and the tricritical Potts models have another fixed point in the p direction. For the crit...

We suggest a fast method for finding possibly overlapping network communities of a desired size and link density. Our method is a natural generalization of the finite-T superparamagnetic Potts clustering introduced by Blatt et al (1996 Phys. Rev. Lett.76 3251) and the annealing of the Potts model with a global antiferromagnetic term recently suggested by Reichard and Bornholdt (2004 Phys. Rev. ...

The Potts model is a well established approach to solve different multi-label problems. The classical Potts prior penalizes the total interface length to obtain regular boundaries. Although the Potts prior works well for many problems, it does not preserve fine details of the boundaries. In recent years, non-local regularizers have been proposed to improve different variational models. The basi...

An important subclass of the min-sum labeling problem (also known as discrete energy minimization or valued constraint satisfaction) is the pairwise min-sum problem with arbitrary unary costs and attractive Potts pairwise costs (also known as the uniform metric labeling problem). In analogy with our recent result, we show that solving the LP relaxation of the Potts min-sum problem is not signif...

We consider a Potts model diluted by fully frustrated Ising spins. The model corresponds to a fully frustrated Potts model with variables having an integer absolute value and a sign. This model presents precursor phenomena of a glass transition in the high-temperature region. We show that the onset of these phenomena can be related to a thermodynamic transition. Furthermore, this transition can...

We introduce the asymmetric random cluster (or ARC) model, which is a graphical representation of the Potts lattice gas, and establish its basic properties. The ARC model allows a rich variety of comparisons (in the FKG sense) between models with diierent parameter values; we give, for example, values (; h) for which the 0's connguration in the Potts lattice gas is dominated by the \+" conngura...

We show how to couple two critical Q-state Potts models to yield a new self-dual critical point. We also present strong evidence of a dense critical phase near this critical point when the Potts models are defined in their completely packed loop representations. In the continuum limit, the new critical point is described by an SU(2) coset conformal field theory, while in this limit of the the c...

The existence and limits of metastable droplets have been calculated using finite-system renormalization-group theory, for q-state Potts models in spatial dimension d=3. dependence the droplet critical sizes on magnetic field, temperature, number states q has calculated. same method also used calculation hysteresis loops across first-order phase transitions these systems. loop shapes deduced as...