Physics Commons^™

Population Annealing: Analysis, Optimization And Application To Glassy Systems, Christopher A. Amey

Doctoral Dissertations

Glasses are physical systems that lack structural order and exhibit extremely slow dynamics, which makes them challenging to study. In this thesis we apply Monte Carlo methods to two distinct glassy systems: the 3D Edwards-Anderson spin glass and a binary hard sphere fluid. While significant progress has been made on theoretical and experimental fronts, much of our current understanding of glasses has come from numerical simulations. Standard Monte Carlo techniques cannot be used to perform equilibrium simulations due to slow dynamics in the glassy regime. As a result, several specialized techniques have been developed in order to simulate such systems, …

Investigation Of Complex Magnetic Phenomena In Spinel Femn2o4, Mnfe2o4, And Nife2o4, Roshan Kumar Nepal

LSU Doctoral Dissertations

Frustrated magnetic systems, where all spin interactions cannot be simultaneously satisfied, have continued to attract interest due to a plethora of novel magnetic states that emerge in them due to frustration and their potential technological applications. Spinel oxides AB₂O₄, where A and B are metal ions) are an excellent testing ground for the exploration of frustrated magnetism. This dissertation presents the experimental investigation of complex magnetic phenomena in the spinel oxides FeMn₂O₄, MnFe₂O₄, and NiFe₂O₄.

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Population Annealing Monte Carlo Studies Of Ising Spin Glasses, Wenlong Wang

Doctoral Dissertations

Spin glasses are spin-lattice models with quenched disorder and frustration. The mean field long-range Sherrington-Kirkpatrick (SK) model was solved by Parisi and displays replica symmetry breaking (RSB), but the more realistic short-range Edwards-Anderson (EA) model is still not solved. Whether the EA spin glass phase has many pairs of pure states as described by the RSB scenario or a single pair of pure states as described by two-state scenarios such as the droplet/scaling picture is not known yet. Rigorous analytical calculations of the EA model are not available at present and efficient numerical simulations of spin glasses are crucial in …

Spin Glass Reflection Of The Decoding Transition For Quantum Error Correcting Codes, Alexey Kovalev, Leonid P. Pryadko

Department of Physics and Astronomy: Faculty Publications

We study the decoding transition for quantum error correcting codes with the help of a mapping to random-bond Wegner spin models. Families of quantum low density parity-check (LDPC) codes with a finite decoding threshold lead to both known models (e.g., random bond Ising and random plaquette Z₂ gauge models) as well as unexplored earlier generally non-local disordered spin models with non-trivial phase diagrams. The decoding transition corresponds to a transition from the ordered phase by proliferation of "post-topological" extended defects which generalize the notion of domain walls to non-local spin models. In recently discovered quantum LDPC code families with …

Replica Exchange Monte Carlo Simulations Of The Ising Spin Glass: Static And Dynamic Properties, Burcu Yucesoy

Open Access Dissertations

Spin glasses have been the subject of intense study and considerable controversy for decades, and the low-temperature phase of short-range spin glasses is still poorly understood. Our main goal is to improve our understanding in this area and find an answer to the following question: Are there only a single pair or a countable infinity of pure states in the low temperature phase of the EA spin glass? To that aim we first start by introducing spin glasses and provide a brief history of their research, then proceed to describe our method of simulation, the parallel tempering Monte Carlo algorithm. …

Interacting Stochastic Processes: From Viciousness To Caging To Force Chains, Shiliyang Xu

Physics - Dissertations

This thesis documents a quest to develop and study several novel interacting stochastic processes. As for the first example, we generalize a system of vicious random walkers in which the only interaction between any two random walkers is that when they intersect, both walkers are annihilated. We define a system of N vicious accelerating walkers with each walker undergoing random acceleration and compute the survival probability distribution for this system. We also define and study a system of N vicious Levy flights in which any two Levy flights crossing one another annihilate each other. The average mean-squared displacement of a …

Observed Superspin-Glass Behavior In Ni0.5zn0.5fe2o4 Nanoparticles, Antony Adair

Open Access Theses & Dissertations

In this investigation we seek to identify the magnetic behavior of Ni0.5Zn0.5Fe2O4 nanoparticles though AC-susceptibility and DC-magnetization measurements. Powder x-ray diffraction was performed to determine the purity and average diameter ( ~ 9nm) of the particles. Aditionally, structure was confirmed by comparison through the International Centre for Diffraction Data's Powder Diffraction File [52] (PDF # 08-0234).

Zero-field cooled and field cooled DC magnetization measurements (bifurcation and blocking temperature), as well as M(H) hysteresis (below and above the blocking temperature) lead us to initially suggest that the material may in fact be superparamagnetic. However, further investigation of the real AC susceptibility …

Percolation In The Sherrington-Kirkpatrick Spin Glass, Jonathan Machta, C. M. Newman, D. L. Stein

Jonathan Machta

We present extended versions and give detailed proofs of results about percolation (using various sets of two-replica bond occupation variables) in Sherrington-Kirkpatrick spin glasses (with zero external field) that were first given in an earlier paper by the same authors. We also explain how ultrametricity is manifested by the densities of large percolating clusters. Our main theorems concern the connection between these densities and the usual spin overlap distribution. Their corollaries are that the ordered spin glass phase is characterized by a unique percolating cluster of maximal density (normally coexisting with a second cluster of nonzero but lower density). The …

Replica Field Theory For Deterministic Models (Ii): A Non-Random Spin Glass With Glassy Behavior, Enzo Marinari, Giorgio Parisi, Felix Ritort

Northeast Parallel Architecture Center

We introduce and study a model which admits a complex landscape without containing quenched disorder. Continuing our previous investigation we introduce a disordered model which allows us to reconstruct all the main features of the original phase diagram, including a low T spin glass phase and a complex dynamical behavior.