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چكيده انگليسي :

Series Expansion Study of Ising Model on Kagome Lattice Zahra Jalalimola z jalalimola@ph iut ac ir April 20 2011 Department of Physics Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language FarsiAssoc Prof Farhad Shahbazi Supervisor Email shahbazi@cc iut ac irAssis Prof Seyed Akbar Jafari Advisor Email akbar jafari@gmail comAbstractIn this work Ising model with different interactions on the two dimensional square and Kagome lattice isstudied using the high temperature series expansion method High temperature series expansion of zero fieldsusceptibility of the ferromagnetic Ising model on the square lattice is derived to order 12 The series of zerofield susceptibility analyzed by the Pade approximation method The critical temperature and criticalexponent of the zero field susceptibility of the ferromagnetic Ising model on square lattice calculated Theresults showed that with increasing order of series critical temperatures approached to a specific value whichis the critical temperature of the Ising model on the square lattice and this value approximately is equal tocritical temperature of the zero field susceptibility of the exactly solved zero field Ising model on the squarelattice Therfore ferromagnetic Ising model on the square lattice showed the ferromagnetic to paramagneticphase transition Using the Pade approximation and increasing order of series critical exponent of the zerofield susceptibility is calculated which is in good agreement with critical exponent of the exactly solved Isingmodel on the square lattice These results are consistent with the universality hypothesis The universalityhypothesis uses for physical systems with the same interaction range and the same space dimention and thesame Hamiltonian symmetry Therefore increasing order of series the obtained critical exponent will beequal to the exactly solved Ising model on square lattice Next high temperature series expansion of the zerofield susceptibility of the ferromagnetic and two ferromagnetic and one ferromagnetic and antiferromagneticinteractions of the Ising model on the two dimensional Kagome lattice derived to order 12 The Kagomelattice is not Bravais lattice which consist of some triangle These series analyzed by the Pade approximationmethod The results showed that ferromagnetic Ising model on kagome lattice have the ferromagnetic toparamagnetic phase transition The critical exponents of the ferromagnetic Ising model on kagome latticehave a good agreement with critical exponent of the zero field susceptibility of the exactly solved Isingmodel on the square lattice The results of the two ferromagnetic Ising model showed that this model hassimilar behavior to ferromagnetic Ising model Therefore these two models have approximately same criticaltemperature The critical exponents of this model consistent with the universality hypothesis have a goodagreement with zero field susceptibility critical exponent of the exactly solved Ising model on the squarelattice But one ferromagnetic and antiferromagnetic interactions of the Ising model on kagome lattice did notshow any phase transition because of the frustration This frustration is related to the geometry of theKagome lattice These two models also have similar behavior The last section vertex functions and zerofield susceptibility of the XY model on the square lattice using the free graph expansions is derived to order8 Then zero field susceptibility of the XY model on square lattice is analyzed by the Pade approximationmethod The results did not show any phase transition for XY model on square lattice Key words Ising model Kagome lattice Zero field susceptibility High temperature seriesexpansion Free graph expansion XY model Ionic disorder

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