Multiple phase transitions in the XY model with nematic-like couplings

Critical behavior of the two-dimensional generalized XY model involving solely nematic-like terms of the second, third and fourth orders is studied by Monte Carlo method. We find that such a system can undergo three successive phase transitions. At higher temperatures there is a phase transition of the Berezinskii–Kosterlitz–Thouless type to the $q=4$ nematic-like phase, followed by two more transitions of the Ising type to the $q=2$ nematic-like and ferromagnetic phases, respectively. The q nematic-like phases are characterized by spin alignments with angles $2k\pi /q$, where $k\le q$ is an integer. The ferromagnetic phase appears at low temperatures even without the presence of magnetic interactions owing to a synergic effect of the nematic-like terms.     

Chern–Simons formulation of three-dimensional gravity with torsion and nonmetricity

We consider various models of three-dimensional gravity with torsion or nonmetricity (metric affine gravity), and show that they can be written as Chern–Simons theories with suitable gauge groups. Using the groups $\mathrm{ISO}(2,1)$, $\mathrm{SL}(2,\mathbb{C})$ and $\mathrm{SL}(2,\mathbb{R})\times \mathrm{SL}(2,\mathbb{R})$, and the fact that they admit two independent coupling constants, we obtain the Mielke–Baekler model for zero, positive and negative effective cosmological constant respectively. Choosing $\mathrm{SO}(3,2)$ as the gauge group, one gets a generalization of conformal gravity that has zero torsion and only the trace part of the nonmetricity. This characterizes a Weyl structure. Finally, we present a new topological model of metric affine gravity in three dimensions arising from an $\mathrm{SL}(4,\mathbb{R})$ Chern–Simons theory.     

Triangle for the entropic index q of non-extensive statistical mechanics observed by Voyager 1 in the distant heliosphere

Tsallis [Physica A 340 (2004) 1) identified a set of numbers, the “q-triplet” ≡ {q_stat, q_sen, q_rel}, for a system described by non-extensive statistical mechanics. The deviation of the q's from unity is a measure of the departure from thermodynamic equilibrium. We present observations of the q-triplets derived from two sets of daily averages of the magnetic field strength B observed by Voyager 1 in the solar wind near 40 A.U. during 1989 and near 85 A.U. during 2002, respectively. The results for 1989 do not differ significantly from those for 2002. We find $q_{\mathrm{stat}}=1.75\pm 0.06$, $q_{\mathrm{sen}}=-0.6\pm 0.2$, and $q_{\mathrm{rel}}=3.8\pm 0.3$.     

New R-matrices from representations of braid-monoid algebras based on superalgebras

In this paper we discuss representations of the Birman–Wenzl–Murakami algebra as well as of its dilute extension containing several free parameters. These representations are based on superalgebras and their baxterizations permit us to derive novel trigonometric solutions of the graded Yang–Baxter equation. In this way we obtain the multiparametric R-matrices associated to the $U_q[\mathit{sl}{(r|2m)}^{(2)}]$, $U_q[\mathit{osp}{(r|2m)}^{(1)}]$ and $U_q[\mathit{osp}{(r=2n|2m)}^{(2)}]$ quantum symmetries. Two other families of multiparametric R-matrices not predicted before within the context of quantum superalgebras are also presented. The latter systems are indeed non-trivial generalizations of the $U_q[D_{n+1}^{(2)}]$ vertex model when both distinct edge variables statistics and extra free-parameters are admissible.