Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session X48: General Statistical Physics |
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Sponsoring Units: GSNP Chair: Allon Percus, Claremont Room: LACC 510 |
Friday, March 9, 2018 8:00AM - 8:12AM |
X48.00001: Constructing ultra-slow glasses in lattice models for reversible computation Lei Zhang, Claudio Chamon, Eduardo Mucciolo, Andrei Ruckenstein We construct a two-dimensional lattice model that lacks any finite |
Friday, March 9, 2018 8:12AM - 8:24AM |
X48.00002: Quantum Annealing to Solve 3-Regular 3-XORSAT on a Lattice Pranay Patil, Stefanos Kourtis, Claudio Chamon, Eduardo Mucciolo, Andrei Ruckenstein Here we show how we can embed the 3-regular 3-XORSAT on a |
Friday, March 9, 2018 8:24AM - 8:36AM |
X48.00003: Tensor Network Algorithms for Counting 2-SAT Solutions Lei Zhang, Justin Reyes, Stefanos Kourtis, Claudio Chamon, Eduardo Mucciolo, Andrei Ruckenstein We present a tensor network method for counting the number of solutions of 2-SAT problems (#2-SAT). We embed 2-SAT problems into a two dimensional square lattice network, and we encode the number of solutions in a tensor trace, which we compute by gradually contracting the tensor network. To optimize the contraction, we use a compression-decimation algorithm to propagate local constraints to longer range before coarse-graining the tensor network. Iterations of these steps allows the network to collapse gradually while containing the tensor dimensions. We compare the results and performance of our tensor-based algorithm with those from the sharpSAT solver based on the DPLL algorithm. |
Friday, March 9, 2018 8:36AM - 8:48AM |
X48.00004: Scaling of Density Fluctuations and Hyperuniformity in One-dimensional Substitution Tilings Erdal Oğuz, Joshua Socolar, Paul Steinhardt, Salvatore Torquato Substitution tilings include periodic, quasiperiodic, limit periodic, and other self-similar structures generated by iterated subdivision and rescaling of a finite set of tiles. We study the scaling of density fluctuations associated with a broad class of substitution rules in one dimension. We show that a simple, heuristic argument for the rate of decay of the integrated Fourier intensity Z(k) at small values of the wavenumber k correctly predicts the scaling of the variance σ2(R) in the number of points contained in intervals of length 2R. The exponent α, defined by Z~kα+1, is determined by the ratio of the second largest and largest eigenvalues of the substitution matrix and can vary between -1 and 3, where α>0 implies a hyperuniform distribution of tile vertices. The hyperuniform class includes tilings that are periodic, quasiperiodic, or limit periodic, including a new class of limit-periodic tilings for which Z approaches zero faster than any power law. Tilings with continuous diffraction spectra may be hyperuniform or may even exhibit stronger fluctuations than a Poisson system. |
Friday, March 9, 2018 8:48AM - 9:00AM |
X48.00005: A Tensor Network Algorithm For The Solution of 3-SAT Justin Reyes, Lei Zhang, Stefanos Kourtis, Claudio Chamon, Andrei Ruckenstein, Eduardo Mucciolo We present a novel tensor network approach to the solution of the 3-SAT problem. We start from a graph visualization of 3-SAT instances and find a suitable embedding of these instances on a reversible circuit defined on a lattice. We then encode the reversible circuit into a two-dimensional rectangular tensor network. We demonstrate a tensor-network compression-decimation algorithm that fully contracts the network and reaches solution in O(n) for tree-like 3-SAT instances. We examine the change of this scaling as a function of the density of cycles in the graph. Finally we compare our algorithms performance to state-of-the-art SAT solvers. |
Friday, March 9, 2018 9:00AM - 9:12AM |
X48.00006: Efficient Contraction of Unstructured Tensor Networks Adam Jermyn Tensor networks have gained significant interest recently as efficient means for numerically representing and manipulating quantum states and as a way to represent classical partition functions. Here we discuss a new method for numerically contracting unstructured finite local tensor networks. Finite size effects and multi-point correlations arise quite naturally from this approach, and we present results for a variety of physically interesting models which are difficult to analyze with other approaches. |
Friday, March 9, 2018 9:12AM - 9:24AM |
X48.00007: Finite-time Complexity of the Persistent Random Walk Adam Svenkeson In the persistent random walk, after each step the walker must decide whether or not to change direction. An unbiased decision leads to the simple random walk and diffusive motion, while a complete bias leads to ballistic motion. The complexity of a process, despite lacking a universal definition, is expected to be higher at the boundary between randomness and determinism, and vanish at either extreme. We study how the complexity of a persistent random walk trajectory varies with both the persistence level and the observation time. We propose that the maximal complexity corresponds to trajectories where the average number of direction-switching events scales as the square root of the observation time. We discuss the reasoning behind this conjecture along with its possible generality. We also analyze fluctuations in particle-tracking measurements of a random walker who selects the optimal persistence value so as to maximize complexity over a given observation time. |
Friday, March 9, 2018 9:24AM - 9:36AM |
X48.00008: Phase transition in Y-shaped particles on triangular lattice Dipanjan Mandal, Trisha Nath, R. Rajesh We study different phases and transitions for the system of Y-shaped particles which are observed in many physical systems such as, igG in human blood, trinapthylene in NOR logic gate etc. |
Friday, March 9, 2018 9:36AM - 9:48AM |
X48.00009: Generic First-order Phase Transition of Orientational Phases with Polyhedral Symmetry Ke Liu, Jonas Greitemann, Lode Pollet In addition to the familiar Heisenberg magnetism, breaking of the rotational symmetry O(3) can actually lead to a large array of orientational orders, classified by three-dimensional point groups. Among this great diversity, the polyhedral orders possess most complex internal symmetries, and represent highly non-trivial ways of spontaneous symmetry breaking. In this presentation, we will utilize a recently introduced lattice Hamiltonian to study the order-disorder phase transition of those polyhedral orders. By means of Monte Carlo simulations, we find that the phase transition is generically first-order for all polyhedral symmetries. Moreover, we show that this universal result is fully consistent with our expectation from a renormalization group approach. We argue that extreme fine tuning is required to promote those transitions to second order ones. We also comment on the nature of phase transitions breaking the O(3) symmetry in general cases. |
Friday, March 9, 2018 9:48AM - 10:00AM |
X48.00010: Normal Form of the 2D Ising Renormalization Group Flows Colin Clement, Archishman Raju, James Sethna We derive the scaling ansatz of the two-dimensional Ising model using Normal Form theory of dynamical systems, showing that no resonances with irrelevant variables can appear in the Renormalization Group flow equations. This clarifies the allowed asymptotic susceptibility and unifies a large literature of corrections to scaling. Our theory is general, describing a machinery for calculating corrections to scaling for any system by first classifying the flows into Universality Families, then adding analytic and singular corrections to parameterize the free energy and observables. In addition to describing currently known corrections to scaling we predict that the flow equations in the microcanonical ensemble will be non-analytic. This subtle and surprising fact indicates that the Renormalization Group may be more natural in some thermal ensembles than in others. |
Friday, March 9, 2018 10:00AM - 10:12AM |
X48.00011: An efficient cluster algorithm for the Ising model in an external field Jaron Kent-Dobias, James Sethna We describe an extension of the Wolff algorithm that works efficiently in the presence of an external magnetic field. Local simulations of the Ising model near its continuous phase transition suffer from critical slowing-down, a power-law increase of the correlation time as the transition is approached. In the absence of an external magnetic field, this has been largely alleviated by cluster algorithms—like the Wolff algorithm—which quickly sample different highly-correlated configurations by flipping large clusters whose size scales with the correlation length. However, existing extensions of these algorithms still suffer from critical slowing-down as the transition is approached with nonzero field, e.g., along the critical isotherm. Our algorithm works in the presence of a field and extends the critical scaling of correlation time the Wolff algorithm achieves at zero field over the entire temperature–field parameter space. As an application, we directly measure observables in the metastable state of the two-dimensional Ising model in the vicinity of its critical point and show that they are described by the scaling theory of the stable state. |
Friday, March 9, 2018 10:12AM - 10:24AM |
X48.00012: Relaxation time scaling of 2D fully frustrated Ising model Tasrief Surungan, Na Xu, Anders Sandvik We probe dynamical aspects of the fully frustrated Ising model on the square |
Friday, March 9, 2018 10:24AM - 10:36AM |
X48.00013: Entropy crisis at zero temperature in two dimensions Ludovic Berthier, Patrick Charbonneau, Andrea Ninarello, Misaki Ozawa, Sho Yaida Long-wavelength translational fluctuations endow two-dimensional glass-forming liquids with dynamical properties markedly different from those of their higher-dimensional counterparts. These long-wavelength fluctuations may also affect the nature of the Kauzmann entropy crisis associated with the rarefaction of metastable states in low dimensions. States with a sufficiently low entropy to discern the role of dimension, however, have thus far been inaccessible to both simulations and experiments. Here, we employ a swap Monte Carlo algorithm that allows the thermalization of polydisperse soft and hard spheres beyond the temperature regime traditionally accessible. By measuring both the configurational entropy and point-to-set correlations we determine that the entropy crisis takes place at finite temperature in three-dimensional systems but at zero temperature in two dimensions. Our results thus suggest that two- and three-dimensional glass formers fundamentally differ and further reinforce the importance of the entropy crisis in all dimensions. |
Friday, March 9, 2018 10:36AM - 10:48AM |
X48.00014: Interplay of Nonlinearity and Strength of Coupling in Classical Open Systems Chitrak Bhadra, Dhruba Banerjee At the classical level, the theory of open system dynamics is characterised by Fluctuation Dissipation Relations (FDR) and Generalised Langevin Equation (GLE). The presence of system nonlinearities has been studied extensively to understand many phenomena in open physical and chemical systems. Here, we show the interplay between the coupling of a probe system and a nonlinear thermal environment, the latter requiring a perturbative treatment due to lack of exact solutions. On one hand, a weak system-bath coupling study reveals the robustness of FDR at zeroeth order with perturbative corrections. The motion is described by an effective GLE with dissipation functions showing non-trivial temperature dependence. The other limit, ie. the strong coupling scenario, drastically extends the standard FDR and breaks time-translation invariance of the noise-correlations. Moreover, the GLE provides non-linear velocity-dependent damping kernels leading to new dynamical fixed points perturbed via nonlinear, nonlocal noise. |
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