6284

5871

كارشناسي ارشد

فيزيك حالت جامد

اصفهان: دانشگاه صنعتي اصفهان، دانشكده فيزيك

1390

نه،83ص.: مصور،جدول،نمودار

ص.ع.به فارسي و انگليسي

فرهاد شهبازي

اكبر جعفري

18/7/90

پيمان صاحب سرا، مجتبي اعلايي

فيزيك

ID5871

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

83 Study of Quantum Phase Transition in Heisenberg Model and Transverse Ising model Using Series Expansion Method Amir Hajibabaei amir hajibabaii@yahoo com April 20 2011 Department of Physics Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Dr Farhad Shahbazi Mail shahbazi@cc iut ac irAbstractGenerally we have two types of phase transition Thermal phase transition and Quantum phasetransition Thermal phase transitions occur due to the competition between energy and entropy ofa system at finite temperature In contrast quantum phase transition occurs at absolute zerotemperature and they are driven by quantum fluctuations At absolute zero temperature a systemlies in its ground state so quantum phase transition occurs between possible competing groundstates for a system in the parameter space of the Hamiltonian Study of the quantum phasetransitions in the absolute zero temperature is a necessary step in the complete understanding ofproperties of materials at higher temperatures In this research we study the quantum phasetransitions in the spin systems One promising methods for studying spin systems is seriesexpansion method Series expansion method consists of high temperature and low temperatureseries expansions and cluster expansion In this thesis we study the cluster expansion method Cluster expansion method is a perturbative method based on non degenerate Rayleigh Schrodinger perturbation theory which is developed for performing high order perturbationseries This method has two types named High temperature type expansion and Low temperaturetype expansion Using cluster expansion method it is possible to perform high order expansionsfor quantities like ground state energy magnetization susceptibility and other quantities Incluster expansion method the problem of performing expansions up to certain order for infinitesystem is reduced to performing series for finite number of small clusters After we obtain series we extrapolate those using standard series analysis methods The aim of extrapolation is to studyproperties of physical system in larger region of the parameter space and study the criticalproperties of the physical system At the end we study the application of the cluster expansionmethod in two spin systems First we study the antiferromagnetic Heisenberg model with nearestand next nearest neighbor interactions on honeycomb lattice We obtained series for ground stateenergy magnetization and parallel susceptibility up to eighth order and then we extrapolateseries for magnetization and obtain a quantum phase transition where magnetization vanishes

فرهاد شهبازي

اكبر جعفري

پيمان صاحب سرا، مجتبي اعلايي