http://www.bibsonomy.org/burst/user/statphys23/algebraBibSonomy BuRST Feed for /user/statphys23/algebra2008-07-21T01:43:24+02:00http://www.bibsonomy.org/bibtex/2e676715358c4e65500abcd8deeb441f2/statphys23statphys232007-06-20T10:16:09+02:00topic-1 hecke model equation affine algebra qkz statphys23 loop <span style="color:#555555;">K. <a href="http://www.bibsonomy.org/author/Shigechi">Shigechi</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 July$A_k$ generalization of the $O(1)$ loop model on a cylinder2007topic-1 hecke model equation affine algebra qkz statphys23 loop We define and study the $A_{k}$ generalization of the $O(1)$ loop model on a cylinder. This model is a new hybrid generalization of the $O(1)$ loop model: defined by the affine Hecke algebra and with cylindric boundary conditions. First, we introduce a new class of the affine Hecke algebra which is characterized by the cylindric relations. We consider the spin representation of the affine Hecke algebra. The affine Hecke generator is obtained by twisting the standard Hecke generator by a diagonal matrix. Second, we consider the representation by the states of the $A_{k}$ generalized model. For this purpose, we introduce a novel graphical depiction, rhombus tiling with an integer on its face, to deal with the Yang-Baxter equation and $q$-symmetrizers. A state of the model is characterized by a path and constructed through the correspondence among an unrestricted path, a rhombus tiling and a word. The cylindric relations become clear by using the rhombus tiling. Finally, we solve the quantum Kniznik-Zamoldchikov (qKZ) equation at the Razumov-Stroganov point. This solution is identified with a special solution of the qKZ equation of the level $1+\frac{1}{k}-k$ constructed from a non-symmetric Macdonald polynomial. The sum rule for this model is written as the product of $k$ Schur functions.http://www.bibsonomy.org/bibtex/29077d0c8e0b9d3413a075e42819c5cf5/statphys23statphys232007-06-20T10:16:09+02:00drinfeld level rule onsager spin xxz non-crossing unity algebra topic-1 loop polynomial statphys23 symmetry chain roots <span style="color:#555555;">T. <a href="http://www.bibsonomy.org/author/Deguchi">Deguchi</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyThe sl(2) loop algebra symmetry of the XXZ spin chain at roots of unity and the Onsager algebra for the super-integrable chiral Potts model2007drinfeld level rule onsager spin xxz non-crossing unity algebra topic-1 loop polynomial statphys23 symmetry chain roots We present an algorithm by which we can calculate the degenerate multiplicity associated with the sl(2) loop algebra symmetry in the energy spectrum of the XXZ spin chain at roots of unity. We formulate an irreducibility criterion for finite-dimensional highest weight representations of the sl(2) loop algebra. Here we remark that the level crossings at roots of unity in the spectral flow correspond to counterexamples of the level non-crossing rule. We then discuss a novel connection between the Onsager algebra of the superintegrable chiral Potts model and the sl(2) loop algebra. We show that the Drinfeld polynomial of a degenerate eigenspace of some higher-spin XXZ spin chain with respect to the sl(2) loop algebra is equivalent to the polynomial (which we call the SCP polynomial after the Superintegrable Chiral Potts model) introduced by McCoy et al and by Baxter. The SCP polynomial characterizes a corresponding subspace showing the Ising-like spectrum for the superintegrable chiral Potts model (The talk is partially in collaboration with A. Nishino. [Ref] Phys. Lett. A Vol. 356 (2006) pp. 366-370 (cond-mat/0605551).)http://www.bibsonomy.org/bibtex/2af036cbdc80081a46e660ccb5747f6f1/statphys23statphys232007-06-20T10:16:09+02:00model grassmann topic-1 statphys23 phase blume diagram capel algebra <span style="color:#555555;">M. <a href="http://www.bibsonomy.org/author/Clusel">Clusel</a> and J.Y. <a href="http://www.bibsonomy.org/author/Fortin">Fortin</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyThe 2D Blume Capel model : fermionisation and phase diagram2007model grassmann topic-1 statphys23 phase blume diagram capel algebra The Blume-Capel model was introduced as an extension of the Ising model, to mimic the physical properties of the liquid mixture of Helium 3 and 4 at low temperature. Mean field theory and Monte Carlo studies show that the phase diagram exhibits a line of second order critical points ending at a tricritical point in the phase diagram. We use a Grassmann algebra technique developed by V. Plechko to derive the exact underlying fermionic field theory for the 2D Blume-Capel. The analysis of this action allows us to characterize the exact critical line.http://www.bibsonomy.org/bibtex/2220463995c2cf2d63a30d688be7f557e/statphys23statphys232007-06-20T10:16:09+02:00computer age algebra hard simulation topic-1 disk absolute fluid reversible methods statphys23 <span style="color:#555555;">J. <a href="http://www.bibsonomy.org/author/Kumi\v{c}\&#039;ak">Kumivc'ak</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyModel cases of irreversibility in reversible systems2007computer age algebra hard simulation topic-1 disk absolute fluid reversible methods statphys23 Two reversible systems with irreversible behavior are studied: a family of generalized baker maps $B_w$ and a 2D hard disk fluid, both acting on the unit square $E$. The numerical simulation of both systems is strictly reversible for any number of iteration steps. The study of the systems enables to trace the emergence of irreversibility without any stochastic assumptions. Each map of the family $B_w$ ($w > 1$) has a rich structure of periodic orbits of any period which are dense in $E$. The relation of periodic orbits to recurrences in the sense of Poincar\'e is demonstrated. Moreover, each map in the family possesses an attractor-repellor pair. The attractors are self-similar, consist of infinite set of parallel lines which cover $E$ densely, have Hausdorff dimension $D_H=2$ and for $w \neq 2$ they are inhomogeneous. There is a precise sense in which one can speak about ``absolute age'' of a state (point in $E$). This notion is then applied to show that it is impossible to define a priori states with very large ``negative age''. Such states can be defined only a posteriori. This gives precise sense to irreversibility in these reversible maps. The 2D hard disk fluid consists of regular polygons having $4n$ sides. They are not allowed to rotate and their interactions are of the hard body type. The requirement that the simulation be reversible necessitates the use of rational values for positions and velocities. The latter then again enable to introduce the notion of absolute age which gives a novel look at the irreversibility. It is observed that with growing $n$ the dynamics approaches the hard disk one with the Maxwell-Boltzmann distribution of speeds. The simulation also enables to demonstrate the gradual appearance of hydrodynamic behavior with growing $n$, retaining at the same time the reversibility of the dynamics.