Global ETD Search
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Showing 1 to 15 of 15 for “"Potts model"”.
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A Dynamical Approach to the Potts Model on Cayley Tree
The Ising model is one of the most important theoretical models in statistical physics, which was originally developed to describe ferromagnetism. A system of magnetic particles, for example, can be modeled as a linear chain in one dimension or a lattice in two dimensions, with one particle at each …
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Introduction to the Glauber dynamics for the Curie-Weiss Potts model
… to the Gibbs distribution of the Curie-Weiss Potts model. Therefore, essential aspects of discrete-time Markov chains on a finite state space are examined, especially their convergence behavior and related mixing times. Furthermore, special emphasis is placed on a consistent and comprehensive …
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Graphical representations of Ising and Potts models: stochastic geometry of the quantum Ising model and the space-time Potts model
… as external conditions are varied. Two models in particular are of great interest to mathematicians, namely the Ising model of a magnet and the percolation model of a porous solid. These models in turn are part of the unifying framework of the random-cluster representation, a model for …
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Solution of sign and complex action problems with cluster algorithms
Two kinds of models are considered which have a Boltzmann weight which is either not real or real but not positive and so standard Monte Carlo methods are not applicable. These sign or complex action problems are solved with the help of cluster algorithms. In each case improved estimators for the …
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Enhanced Potts Models for Improved Computational Protein Design
… framework that outperforms state-of-the-art models in native sequence recovery. For a target structure, the model outputs a Potts model, an energy table describing the self and pairwise energetic contributions for all amino acids at all positions. In this thesis, I investigate approaches for …
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Physical Models in Community Detection with Applications to Identifying Structure in Complex Amorphous Systems
… an exceptionally accurate spin-glass-type Potts model for the graph theoretic problem of community detection. With a simple algorithm, we find that our approach is exceptionally accurate, robust to the effects of noise, and competitive with the best currently available algorithms in terms …
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On the partition function for the three-dimensional Ising model
… the critical behaviour of lattice spin models such as the three-dimensional Ising model in the thermodynamic limit. The exact partition functions (typically summed over the order of 1075 states) for finite simple cubic Ising lattices are computed using a transfer matrix approach. Q-state …
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Phase transitions and critical phenomena: Universality and global multicritical phase diagrams from position-space renormalization-group studies
… the local critical properties of rather simple models. After presenting background on phase transitions and reviewing the PSRG procedure in general, we extend this approach to more complicated systems anq global multicritical behavior by two specific studies. First, we introduce the concept of …
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Model studies aimed toward constructing PI3K pathways in leukemia T-cells from shRNA knockdowns
… on a known small network and tested an inverse Potts model for reconstructing the network based on correlations from the simulation output. We found the method did not infer the small network properly, but did produce several patterns that indicate it may have potential for revealing something …
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Variational Algorithms and Resources for Near-Term Quantum Simulation
… ansatz using the critical transverse-field Ising model to optimize circuit parameters, numerically test the noise resilience of observables and customized error mitigation techniques using a local gate noise model, and demonstrate the robustness of local subregion preparation on an existing …
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Studying the effect of Cu microstructure on electromigration reliability using statistical simulation
… Most of the earlier studies of EM modeling have assumed an averaged diffusivity measured across the underlying crystallographic microstructure. The objective of this thesis is to study the effect of microstructure on EM reliability by modeling of the diffusivity corresponding to …
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In silico vaccine design for hepatitis C: A computational platform for fighting disease
Hepatitis C virus (HCV) infects 2-3% of the world's population. It is a major cause of liver morbidity and mortality and a scourge to global public health. Despite more than 20 years of research, only recently have effective treatments been developed and a vaccine remains elusive. The high cost of …
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Corner Transfer Matrix approach to the Yang-Lee Singularity in the 2D Ising Model
… field analytic continuation of the 2D Ising model near the Yang-Lee singularity. The exact location of the singularity is not known precisely, and one of the results produced is an improved quality estimate of its location $\xi_0 \approx i0.1893506$. Another primary result is the numerical …
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Corner Transfer Matrix approach to the Yang-Lee Singularity in the 2D Ising Model
… field analytic continuation of the 2D Ising model near the Yang-Lee singularity. The exact location of the singularity is not known precisely, and one of the results produced is an improved quality estimate of its location $\xi_0 \approx i0.1893506$. Another primary result is the numerical …
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Competitive Nucleation in Nanoclusters
… nucleation event. Competitive nucleation is modeled using a two dimensional Potts model undergoing heterogeneous nucleation on to a nanoscale impurity. The rates of formation of the different stable phases are calculated using transition state theory and compared with the rates obtained from …