Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session Y33: Statistical Physics:Dynamics and Transitions |
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Sponsoring Units: GSNP Chair: AlfredHubler, University of Illinois Room: Baltimore Convention Center 336 |
Friday, March 17, 2006 8:00AM - 8:12AM |
Y33.00001: Higher Order Phase Transitions and Tachyon Condensation Pradeep Kumar, Avadh Saxena, Avinash Khare We discuss the similarities (and the differences) between the models which describe a $p$'th order phase transition (in the Ehrenfest sense) and that which describes tachyon condensation in string theory. Using the appropriate free energy for the two systems, we obtain exact domain wall solutions and study their stability for some cases. Extrapolating this analogy, we suggest that the tachyon condensation is analogous to the celebrated Kosterlitz-Thouless transition. It has been suggested that the superconducting transition in BKBO may be of order four. Similarly, the Ising ferromagnet on a Cayley tree and a model by Gross and Witten in particle physics are believed to be order three. [Preview Abstract] |
Friday, March 17, 2006 8:12AM - 8:24AM |
Y33.00002: Analysis of the long-range random field quantum anti-ferromagnetic Ising model : Some exact results Jun-ichi Inoue, Arnab Das, Bikas K. Chakrabarti With the realization in the mid last century, that the Neel state cannot be the ground state of a quantum Heisenberg anti-ferromagnet (AF), considerable effort has gone in search of and in understanding the nature of the ground stateof such and similar quantum AF. Since early 1960s, quantum spin systems described by Ising model in a transverse tunneling field was investigated, particularly because of easy mapping of the quantum system to its equivalent classical system and some cases of exact solubility. However, there has, so far, been very few models with AF interactions. It is well-known, the transverse Ising model with long range interactions is solved exactly, even if the system has some special kind of quenched disorder, like in spin glasses. However, it is not so easy to consider the AF version of the model due to a lack of sub-lattice to capture the Neel ordering at low temperature. In this paper, we introduce and study a solvable quantum AF model. In our model system each spin is influenced by the infinite range AF interactions in a transverse field. We also consider the case under the random fields. By introducing two sub-groups of the spin system, we describe the system by means of the effective single spin Hamiltonian and solve it exactly. [Preview Abstract] |
Friday, March 17, 2006 8:24AM - 8:36AM |
Y33.00003: Lattice dimers and the tilting transition Ercan Kamber, Jan\'{e} Kondev We study the statistics of dimer coverings of the honeycomb lattice by Monte Carlo simulations. Dimer configurations are given by placing dimers on adjacent sites with the constraint that every site is covered by one and only one dimer. We implement the pocket algorithm [1], which is believed to be ergodic on the space of dimer coverings. The pocket algorithm enables global updates of dimer configurations without violating the packing constraint. Dimer configurations can be mapped to a height model [2], which associates a discrete interface with every dimer covering. If the dimers are aligned along one direction of the honeycomb lattice, the height interface will be tilted. We investigate the fluctuations of the associated height model, when the system undergoes a transition from an untilted rough interface to a tilted smooth interface. We impose a fixed tilt of the interface and measure fluctuations of the height. For a tilted surface the height fluctuations are anisotropic with a variance that increases logarithmically with system size. We compute the effective stiffness of the interface and find that it increases with increasing tilt. [1] W. Krauth , R. Moessner, Phys. Rev. B 67, 2003. [2] H.W.J. Blote , H.J. Hilhorst , J. Phys. A 15, 1982. [Preview Abstract] |
Friday, March 17, 2006 8:36AM - 8:48AM |
Y33.00004: A non-Hermitian analysis of strongly correlated quantum systems Yuichi Nakamura, Naomichi Hatano We study a non-Hermitian generalization of strongly correlated quantum systems in which the transfer energy of electrons is asymmetric. Hatano and Nelson[1] applied this technique to non-interacting random electron systems. They related a non-Hermitian critical point to the inverse localization length of the Hermitian systems. We here conjecture that we can obtain in the same way the correlation length of Hermitian interacting non-random systems[2]. We show for the Hubbard model and the antiferromagnetic XXZ model in one dimension that the non-Hermitian critical point of the ground state, where the energy gap vanishes, is equal to the inverse correlation length. We also show that the conjecture is consistent with numerical results for S=1/2 frustrated quantum spin chains with the nearest- and next-nearest-neighbor interactions including the Majumdar-Ghosh model[3]. [1] N. Hatano and D. R. Nelson, PRL 77 (1996) 570; PRB 56 (1997) 8651. [2] Y. Nakamura and N. Hatano, Physica B, accepted. [3] C. K. Majumdar and D. K. Ghosh, J. Phys. C3 (1970) 911; J. Math. Phys. 10 (1969) 1388, 1399. [Preview Abstract] |
Friday, March 17, 2006 8:48AM - 9:00AM |
Y33.00005: Spectrum of superintegrable chiral Potts model and L(sl$_{2})$ symmetry in associated XXZ-type spin chain Akinori Nishino, Tetsuo Deguchi We study the correspondence between the Ising-like spectra of superintegrable N-state chiral Potts (SCP) model [1,2] and the energy degenerate subspaces of XXZ-type spin chain, called nilpotent Bazhanov-Stroganov (NBS) model [3], whose transfer matrix commutes with the SCP transfer matrix. We show that, if the number of sites is a multiple of N, the NBS model has a loop algebra L(sl$_{2})$ symmetry in the subspace with Z$_{N}$-charge Q=0. Applying the approach [4] to the case, we obtain the dimension of L(sl$_{2})$-degenerate subspaces through the calculation of Drinfeld polynomials. The Drinfeld polynomials are in fact identified with Baxter's polynomials [2] characterizing the SCP's Ising-like spectra, which shows that each subspace with the Ising-like spectra have the same dimension as the corresponding L(sl$_{2})$-degenerate subspace of NBS model. [1] G. Albertini, B. M. McCoy, J. H. H. Perk and S. Tang, Nucl. Phys. B 314 (1989) 741. [2] R. J. Baxter, J. Statist. Phys. 57 (1989) 1. [3] V. V. Bazhanov and Yu. G. Stroganov, J. Statist. Phys. 59 (1990) 803. [4] T. Deguchi, cond-mat/0503564. [Preview Abstract] |
Friday, March 17, 2006 9:00AM - 9:12AM |
Y33.00006: Alignment of Rods and Partition of Integers, an Exact Solution Eli Ben-Naim We study dynamical alignment of rods, a process in which rods become parallel by pairwise interactions, and also, wiggle in a diffusive manner. With strong diffusion, the system is disordered, but with weak diffusion, the system is ordered. We present an exact solution for the nonlinear and nonlocal kinetic theory of this alignment process, at the steady-state. The Fourier transform is expressed as a function of the order parameter, and generally, the Fourier modes decay exponentially with the wave number. The order parameter is found as a root of a closed equation. This solution involves iterated partitions of the integer numbers. [Preview Abstract] |
Friday, March 17, 2006 9:12AM - 9:24AM |
Y33.00007: Integrable Chiral Potts Model Alive and Well Jacques H.H. Perk, Helen Au-Yang \noindent About two decades have passed since the introduction of the integrable chiral Potts model, parametrized by a high-genus curve [1,2]. In spite of this mathematical complication, several exact results have been obtained since, culminating in Baxter's proof [3,4] of the conjecture for the order parameters. Here we shall discuss several other results. First we shall show how the model fits in the phase diagram of a more general nonintegrable chiral Potts model and what we have learned about critical exponents and scaling behavior. Next, we shall mention some mathematical implications. Finally, we shall discuss our preliminary work on the pair correlation functions. \begin{enumerate} \item{H.\ Au-Yang, B.M.\ McCoy, J.H.H.\ Perk, S.\ Tang and M.-L.Yan, Phys. Lett. {\bf 123}, 219--223 (1987).} \item{R.J.\ Baxter, J.H.H.\ Perk and H.\ Au-Yang, Phys. Lett. {\bf 128}, 138--142 (1988).} \item{R.J.\ Baxter, J. Stat. Phys. {\bf 120}, 1--36, (2005).} \item{C. Day, Physics Today, {\bf 58} \# 11, 19--21 (November 2005).} \item{H.\ Au-Yang and J.H.H.\ Perk, to be published.} \end{enumerate} [Preview Abstract] |
Friday, March 17, 2006 9:24AM - 9:36AM |
Y33.00008: Statistics of work done by flow on a polymer Michael Chertkov We study polymer immersed in a flow and subjected to thermal fluctuations. Shear flow as well as chaotic flows are considered. Flow does work on the polymer while the polymer in its turn releases access of energy into heat. Statistics of work/heat production is analyzed in this non-equilibrium (off detailed balance) but steady problem theoretically and numerically. Analogs of fluctuation theorem and Jarzynski equality for annealed/quenched averaging procedures applied to the system are established. We also discuss possible generalization of this approach/study to more complex non-equilibrium problems, like turbulence. This is a joint work with A. Puliafito (INLN, Nice) and K. Turitsyn (Landau Inst., Moscow). [Preview Abstract] |
Friday, March 17, 2006 9:36AM - 9:48AM |
Y33.00009: On Harmonic Measure of Critical Curves Ilia Rushkin, Eldad Bettelheim, Ilya Gruzberg, Paul Wiegmann Fractal geometry of critical curves appearing in 2D critical systems is characterized by their harmonic measure. For systems described by conformal field theories with central charge $c\leq 1$ the scaling exponents of the harmonic measure have been computed by B. Duplantier [Phys. Rev. Lett. {\bf 84}, 1363 (2000)] by relating the problem to boundary two-dimensional gravity. We present a simple argument connecting the harmonic measure of critical curves to operators obtained by fusion of primary fields, and compute characteristics of the fractal geometry by means of regular methods of conformal field theory. The method is not limited to theories with $c\leq 1$. [Preview Abstract] |
Friday, March 17, 2006 9:48AM - 10:00AM |
Y33.00010: Methods of calculating Ruelle-Pollicott resonances Elizabeth Keller, Mark Srednicki We develop a method to compute the Ruelle-Pollicott resonances for the classical perturbed cat map. Using sine and cosine basis states, we calculate the matrix elements of the Frobenius-Perron operator and find the eigenvalues of the resulting matrix. Because the matrix is sparse, we are able to reach sufficiently large matrix dimensions to obtain stable, convergent values for the Ruelle-Pollicott resonances. [Preview Abstract] |
Friday, March 17, 2006 10:00AM - 10:12AM |
Y33.00011: Phase Transition of a Dynamical System with a Bi-Directional, Instantaneous Coupling to a Virtual System Vadas Gintautas, Alfred Hubler As worldwide computer resources increase in power and decrease in cost, real-time simulations of physical systems are becoming increasingly prevalent, from laboratory models to stock market projections and entire ``virtual worlds'' in computer games. Often, these systems are meticulously designed to match real-world systems as closely as possible. We study the limiting behavior of a virtual horizontally driven pendulum coupled to its real-world counterpart, where the interaction occurs on a time scale that is much shorter than the time scale of the dynamical system. We find that if the physical parameters of the virtual system match those of the real system within a certain tolerance, there is a qualitative change in the behavior of the two-pendulum system as the strength of the coupling is increased. Applications include a new method to measure the physical parameters of a real system and the use of resonance spectroscopy to refine a computer model. As virtual systems better approximate real ones, even very weak interactions may produce unexpected and dramatic behavior. The research is supported by the National Science Foundation Grant No. NSF PHY 01-40179, NSF DMS 03-25939 ITR, and NSF DGE 03-38215. [Preview Abstract] |
Friday, March 17, 2006 10:12AM - 10:24AM |
Y33.00012: Wave stability on one-dimensional non-linear lattices Chia-Chen Chang, Gerald D. Mahan We report the results of our stability analysis of exact travling wave solutions for two non-linear mono-atomic lattices in one dimension. One lattice has nearest-neighbor potential energy containg quadratic and quartic terms (Fermi-Pasta-Ulam model). The other lattice has potential energy which goes as $cosh(q)$, a generalization of the Toda lattice. These exact traveling wave solutions have wave lengths that are commensurate with the lattice constant. It is found that on the quadratic-quartic lattice, the traveling wave solutions are unstable. For the $cosh(q)$ lattice, on the other hand, the solutions are stable. [Preview Abstract] |
Friday, March 17, 2006 10:24AM - 10:36AM |
Y33.00013: Effective Masses of Vector Polarons Charles Foell, Dennis Clougherty We consider the vector polarons of a one-dimensional model of an electron in a doubly (or nearly) degenerate band that couples to two elastic distortions, as described previously by Clougherty and Foell [1]. A variational approach is used to analytically and numerically calculate effective masses of the three types of vector polarons. [1] D. P. Clougherty and C. A. Foell, Phys. Rev. B 70, 052301 (2004). [Preview Abstract] |
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