HW4 - Physics 127B Homework Set 4(due February 10 MONTE...

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Unformatted text preview: Physics 127B Homework Set 4: (due February 10) MONTE CARLO SIMULATION FOR 1-DIMENSIONAL ISING MODEL Carry out a Monte Carlo simulation on the computer (canonical ensemble, Metropolis algorithm) for the 1-dimensional Ising model with N = 100 spins and periodic boundary conditions: S 1 S 2 S 3 S i S N 1 2 3 N i (lattice sites) (spin variables) (periodic boundary condition) The spin variable S i at site i can take values 1, corresponding to spin up or down. A configura- tion (state) is specified by specifying the values of all spin variables S 1 ,... ,S N . The energy of a configuration is given by E ( S 1 ,...,S N ) =- J N summationdisplay i =1 S i S i +1- h N summationdisplay i =1 S i , (1) where S N +1 S 1 (periodic boundary condition), J > 0 is the coupling constant (ferromagnetic), and h is the magnetic field (positive or negative, in units of energy). The magnetization of the system at temperature T and magnetic field h is given by M ( T,h ) = (Bigg N summationdisplay i =1...
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