Date of Award

8-2024

Document Type

Campus Access Thesis

Degree Name

Master of Science (MS)

Department

Physics, Applied

First Advisor

Olga Goulko

Second Advisor

Niraj Kumar

Third Advisor

Akira Sone

Abstract

This thesis investigates the critical temperatures in the two-dimensional grasshopper Ising model, a novel system derived from ”The Grasshopper Problem,” which has its origin in analyzing Bell inequalities. Our study focuses on a discrete version of the grasshopper problem, obtained by discretizing its planar variant, which results in an Ising model with unique characteristics that set it apart from traditional Ising models in statistical physics. By employing Monte Carlo simulations, we examine the temperature dependence of the grasshopper model and determine the critical temperatures for various fixed-range interactions. We find that the grasshopper model shows a phase transition from a cogwheel structure to a disk with fuzzy boundary when the temperature is increased. We also take on a start to establishing a relationship between the range of interaction and critical temperature in the grasshopper model. Our findings contribute to the broader understanding of statistical mechanics and Bell inequalities, bridging the gap between classical spin systems and quantum phenomena. This research advances our knowledge on this novel class of Ising models and also provides a foundation for future studies in related fields.

Comments

Free and open access to this Campus Access Thesis is made available to the UMass Boston community by ScholarWorks at UMass Boston. Those not on campus and those without a UMass Boston campus username and password may gain access to this thesis through resources like Proquest Dissertations & Theses Global (https://www.proquest.com/) or through Interlibrary Loan. If you have a UMass Boston campus username and password and would like to download this work from off-campus, click on the "Off-Campus UMass Boston Users

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Additional Files

Money_MS_Thesis_Signatory_Page (1).pdf (207 kB)

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