Related papers: Potts Partition Function Zeros and Ground State En…
A new approach to black hole thermodynamics is proposed in Loop Quantum Gravity (LQG), by defining a new black hole partition function, followed by analytic continuations of Barbero-Immirzi parameter to $\gamma\in i\mathbb{R}$ and…
For any integers $d,q\ge 3$, we consider the $q$-state ferromagnetic Potts model with an external field on a sequence of expander graphs that converges to the $d$-regular tree $\mathtt{T}_d$ in the Benjamini-Schramm sense. We show that…
The surface and bulk properties of the two-dimensional Q > 4 state Potts model in the vicinity of the first order bulk transition point have been studied by exact calculations and by density matrix renormalization group techniques. For the…
We investigate the critical behaviour of the three-dimensional, three state Potts model in presence of a negative external field h, i.e. disfavouring one of the three states. A genuine phase transition is present for all values of |h|,…
All local bond-state densities are calculated for q-state Potts and clock models in three spatial dimensions, d=3. The calculations are done by an exact renormalization group on a hierarchical lattice, including the density recursion…
The multivariate Tutte polynomial (known to physicists as the Potts-model partition function) can be defined on an arbitrary finite graph G, or more generally on an arbitrary matroid M, and encodes much important combinatorial information…
Counting problems, determining the number of possible states of a large system under certain constraints, play an important role in many areas of science. They naturally arise for complex disordered systems in physics and chemistry, in…
We study the critical behavior of the random q-state Potts model in the large-q limit on the diamond hierarchical lattice with an effective dimensionality $d_{\rm eff} > 2$. By varying the temperature and the strength of the frustration the…
The spin-half pyrochlore Heisenberg antiferromagnet (PHAF) is one of the most challenging problems in the field of highly frustrated quantum magnetism. Stimulated by the seminal paper of M.~Planck [M.~Planck, Verhandl. Dtsch. phys. Ges.…
The partition function of the random energy model at inverse temperature $\beta$ is a sum of random exponentials $Z_N(\beta)=\sum_{k=1}^N \exp(\beta \sqrt{n} X_k)$, where $X_1,X_2,...$ are independent real standard normal random variables…
The finite lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the $q$-state Potts model to order $z^{56}$ (i.e. $u^{28}$), $z^{47}$, $z^{43}$,…
Suppose $v(x,y):\mathbb C\rightarrow \mathbb R$ is an entire harmonic polynomial with no critical points in the right half plane. Let $z_1, z_2\in\mathbb C$ lie on a level set of $v$ , and assume ${\rm Re}(z_2)>{\rm Re}(z_1)\geq0$. We give…
The phase transition in the q-state Potts model with homogeneous ferromagnetic couplings is strongly first order for large q, while is rounded in the presence of quenched disorder. Here we study this phenomenon on different two-dimensional…
We consider Potts model hypersurfaces defined by the multivariate Tutte polynomial of graphs (Potts model partition function). We focus on the behavior of the number of points over finite fields for these hypersurfaces, in comparison with…
An exact analytical solution of generalized three-state double-chain Potts model with multi-spin interactions which are invariant under cyclic shift of all spin values is obtained. The partition function in a finite cyclically closed strip…
The chromatic polynomial P_G(q) of a loopless graph G is known to be nonzero (with explicitly known sign) on the intervals (-\infty,0), (0,1) and (1,32/27]. Analogous theorems hold for the flow polynomial of bridgeless graphs and for the…
The $S=1/2$ hyperkagome-lattice Heisenberg antiferromagnet allows to study the interplay of geometrical frustration and quantum as well as thermal fluctuations in three dimensions. We use 16 terms of a high-temperature series expansion…
We study the q-state Potts model on the simple cubic lattice with ferromagnetic interactions in one lattice direction, and antiferromagnetic interactions in the two other directions. As the temperature T decreases, the system undergoes a…
We study the number of dimer-monomers $M_d(n)$ on the Tower of Hanoi graphs $TH_d(n)$ at stage $n$ with dimension $d$ equal to 3 and 4. The entropy per site is defined as $z_{TH_d}=\lim_{v \to \infty} \ln M_d(n)/v$, where $v$ is the number…
An exact solution of one-dimensional lattice gauge theory at finite temperature and non-zero chemical potential is reviewed for the gauge groups $G=Z(N),U(N),SU(N)$ for all values of $N$ and the number of fermion flavors $N_f$. Calculated…