نيروي كازيمير در سيستم هاي ترموديناميكي

چكيده انگليسي :

Casimir Force in Thermodynamic Systems Arezoo Sheibany a sheibany@ph iut ac ir Date of Submission 13 3 2011 Department of Physics Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Behrouz Mirza b mirza@cc iut ac ir Abstract In this thesis we calculate Casimir force in one dimensional Ising model with four boundary conditions periodic anti periodic free and fix in presence of magnetic field two dimensional Ising model in presence of magnetic field and patts model with three boundary conditions periodic free and fix in presence of magnetic field There are many systems in nature which are subjected to fluctuations of thermal or quantum origin For such systems under certain physical conditions Casimir forces created by the confinement of fluctuations exist and have been calculated The usual way to obtain the Casimir forces uses equilibrium techniques and is therefore valid only for systems in thermodynamic equilibrium Casimir forces for these systems are calculated in the spirit of the original work of H G Casimir for the electromagnetic case The method takes as a starting point Hamiltonian of the system from which the partition function is calculated either directly or using functional integration In the calculation of the partition function one must take into account the boundary conditions that is the macroscopic bodies which are immersed in the system The partition function of the system will have different values for different configurations e g different separations of the objects Once the partition function has been obtained its logarithm provides the free energy F The final step required to obtain the Casimir force is the calculation of the pressure as the difference in the free energy when the configurations of the macroscopic bodies change for example changing their position distance or sizes Ising model simple minded lattice statistical model has been proposed by Lenz and five years later has been exactly solved by Ising for the particular case of the linear chain In this thesis we calculate partition function of one dimensional Ising model then calculate free energy and Casimir force The two dimensional Ising model in a nonzero magnetic field is a well known unsolved problem in statistical mechanics Fisher produced a remarkable solution of a super exchange anti ferromagnetic Ising model in the presence of a nonzero field The Fisher model is defined on a decorated square lattice where there is an external magnetic field applied to decorating spins which interact via super exchange interactions In this thesis we consider similar super exchange models on the kagome lattice Our main result is an equivalence of partition function of a kagome Ising model to the partition function of a honeycomb Ising model in zero field a result which renders the model soluble We calculate partition function of two dimensional kagome Ising model then calculate free energy and Casimir force The Q state Potts model is a generalization of the Ising model The Potts model is also related to other outstanding problems in physics and mathematics Recently the exact results on the Yang Lee zeros of the ferromagnetic Potts model have been found using the one dimensional model Glumac and Uzelac found the eigen values of the transfer matrix of the one dimensional Potts model for general Q In this thesis we calculate partition function of one dimensional Patts model then calculate free energy and Casimir force Key Words Casimir force Ising model Boundary conditions Patts model Kagome lattice

شيباني، آرزو

نيروي كازيمير در سيستم هاي ترموديناميكي

مدل آيزينگ , مدل پاتس , انرژي آزاد , ميدان مغناطيسي , شرايط مرزي و مواد فرومغناطيس و پاد فرومغناطيس