Complex-temperature phase diagram of Potts and RSOS models

We study the phase diagram of Q-state Potts models, for Q=4 cos^2(PI/p) a Beraha number (p>2 integer), in the complex-temperature plane. The models are defined on L x N strips of the square or triangular lattice, with boundary conditions on the Potts spins that are periodic in the longitudinal (N) direction and free or fixed in the transverse (L) direction. The relevant partition functions can then be computed as sums over partition functions of an A\_{p-1} type RSOS model, thus making contact with the theory of quantum groups. We compute the accumulation sets, as N -> infinity, of partition function zeros for p=4,5,6,infinity and L=2,3,4 and study selected features for p>6 and/or L>4. This information enables us to formulate several conjectures about the thermodynamic limit, L -> infinity, of these accumulation sets. The resulting phase diagrams are quite different from those of the generic case (irrational p). For free transverse boundary conditions, the partition function zeros are found to be dense in large parts of the complex plane, even for the Ising model (p=4). We show how this feature is modified by taking fixed transverse boundary conditions.Comment: 60 pages, 16 figures, 2 table

Phase diagram of the chromatic polynomial on a torus

We study the zero-temperature partition function of the Potts antiferromagnet (i.e., the chromatic polynomial) on a torus using a transfer-matrix approach. We consider square- and triangular-lattice strips with fixed width L, arbitrary length N, and fully periodic boundary conditions. On the mathematical side, we obtain exact expressions for the chromatic polynomial of widths L=5,6,7 for the square and triangular lattices. On the physical side, we obtain the exact ``phase diagrams'' for these strips of width L and infinite length, and from these results we extract useful information about the infinite-volume phase diagram of this model: in particular, the number and position of the different phases.Comment: 72 pages (LaTeX2e). Includes tex file, three sty files, and 26 Postscript figures. Also included are Mathematica files transfer6_sq.m and transfer6_tri.m. Final version to appear in Nucl. Phys.

Selfduality for coupled Potts models on the triangular lattice

We present selfdual manifolds for coupled Potts models on the triangular lattice. We exploit two different techniques: duality followed by decimation, and mapping to a related loop model. The latter technique is found to be superior, and it allows to include three-spin couplings. Starting from three coupled models, such couplings are necessary for generating selfdual solutions. A numerical study of the case of two coupled models leads to the identification of novel critical points

Exact results for the zeros of the partition function of the Potts model on finite lattices

The Yang-Lee zeros of the Q-state Potts model are investigated in 1, 2 and 3 dimensions. Analytical results derived from the transfer matrix for the one-dimensional model reveal a systematic behavior of the locus of zeros as a function of Q. For 1<Q<2 the zeros in the complex $x=\exp(\beta H_q)$ plane lie inside the unit circle, while for Q>2 they lie outside the unit circle for finite temperature. In the special case Q=2 the zeros lie exactly on the unit circle as proved by Lee and Yang. In two and three dimensions the zeros are calculated numerically and behave in the same way. Results are also presented for the critical line of the Potts model in an external field as determined from the zeros of the partition function in the complex temperature plane.Comment: 15 pages, 6 figures, RevTe

Hypophysitis induced by immune checkpoint inhibitors in a Scottish melanoma population:Immune checkpoint inhibitor toxicity

Aim: This study aims to determine the incidence of all immune-mediated adverse events (IMAEs) with a focus on hypophysitis in patients with metastatic melanoma receiving immune checkpoint inhibitors (ICI). Methods: 51 patients with metastatic melanoma who received immune checkpoint inhibitors (ipilimumab, pembrolizumab and nivolumab) in Ninewells Hospital, Dundee between 2014 and 2018 were identified. Patient demographic data and outcomes were recorded retrospectively. Results: A total of 6 patients (11.7%) developed hypophysitis, while 15 patients (29.4%) developed IMAEs. A significant improvement in overall survival (p = 0.03) and progression-free survival (p = 0.041) was seen in patients who developed IMAEs compared with those who did not. Conclusion: This study demonstrates a high rate of hypophysitis in melanoma patients receiving ipilimumab. Careful monitoring of symptoms is crucial to detect and appropriately manage IMAEs

MEME-LaB : motif analysis in clusters

Genome-wide expression analysis can result in large numbers of clusters of co-expressed genes. While there are tools for ab initio discovery of transcription factor binding sites, most do not provide a quick and easy way to study large numbers of clusters. To address this, we introduce a web-tool called MEME-LaB. The tool wraps MEME (an ab initio motif finder), providing an interface for users to input multiple gene clusters, retrieve promoter sequences, run motif finding, and then easily browse and condense the results, facilitating better interpretation of the results from large-scale datasets

Character decomposition of Potts model partition functions. I. Cyclic geometry

We study the Potts model (defined geometrically in the cluster picture) on finite two-dimensional lattices of size L x N, with boundary conditions that are free in the L-direction and periodic in the N-direction. The decomposition of the partition function in terms of the characters K\_{1+2l} (with l=0,1,...,L) has previously been studied using various approaches (quantum groups, combinatorics, transfer matrices). We first show that the K\_{1+2l} thus defined actually coincide, and can be written as traces of suitable transfer matrices in the cluster picture. We then proceed to similarly decompose constrained partition functions in which exactly j clusters are non-contractible with respect to the periodic lattice direction, and a partition function with fixed transverse boundary conditions.Comment: 21 pages, 4 figure