PHY 341641 Thermodynamics and Statistical Physics Lecture 18

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PHY 341/641 Thermodynamics and Statistical Physics Lecture 18 Methodologies of statistical mechanics. (Chapter 5

PHY 341/641 Thermodynamics and Statistical Physics Lecture 18 Methodologies of statistical mechanics. (Chapter 5 in STP) Ising model systems a. Definition b. Exact solution for 1 -dimension c. Mean field solution 9/25/2020 PHY 341/641 Spring 2012 -- Lecture 18 1

9/25/2020 PHY 341/641 Spring 2012 -- Lecture 18 2

9/25/2020 PHY 341/641 Spring 2012 -- Lecture 18 2

Statistical mechanics of spin ½ systems 9/25/2020 PHY 341/641 Spring 2012 -- Lecture 16

Statistical mechanics of spin ½ systems 9/25/2020 PHY 341/641 Spring 2012 -- Lecture 16 3

Calculation of Z 1 Thermodynamic functions: 9/25/2020 PHY 341/641 Spring 2012 -- Lecture 16

Calculation of Z 1 Thermodynamic functions: 9/25/2020 PHY 341/641 Spring 2012 -- Lecture 16 4

Independent particle system Interacting particle system – Ising model 9/25/2020 PHY 341/641 Spring 2012

Independent particle system Interacting particle system – Ising model 9/25/2020 PHY 341/641 Spring 2012 -- Lecture 18 5

Ising model for H = 0 and N=2 9/25/2020 PHY 341/641 Spring 2012 --

Ising model for H = 0 and N=2 9/25/2020 PHY 341/641 Spring 2012 -- Lecture 18 6

Ising model for H ≠ 0 and N=2 9/25/2020 PHY 341/641 Spring 2012 --

Ising model for H ≠ 0 and N=2 9/25/2020 PHY 341/641 Spring 2012 -- Lecture 18 7

Partition function for 1 -dimensional Ising system of N spins with periodic boundary conditions

Partition function for 1 -dimensional Ising system of N spins with periodic boundary conditions (s. N+1=s 1) 9/25/2020 PHY 341/641 Spring 2012 -- Lecture 18 8

1 -dimensional Ising system of N spins with periodic boundary conditions (s. N+1=s 1)

1 -dimensional Ising system of N spins with periodic boundary conditions (s. N+1=s 1) (continued) 9/25/2020 PHY 341/641 Spring 2012 -- Lecture 18 9

1 -dimensional Ising system of N spins with periodic boundary conditions (s. N+1=s 1)

1 -dimensional Ising system of N spins with periodic boundary conditions (s. N+1=s 1) (continued) 9/25/2020 PHY 341/641 Spring 2012 -- Lecture 18 10

1 -dimensional Ising system of N spins with periodic boundary conditions (s. N+1=s 1)

1 -dimensional Ising system of N spins with periodic boundary conditions (s. N+1=s 1) (continued) 9/25/2020 PHY 341/641 Spring 2012 -- Lecture 18 11

1 -dimensional Ising system of N spins with periodic boundary conditions (s. N+1=s 1)

1 -dimensional Ising system of N spins with periodic boundary conditions (s. N+1=s 1) (continued) 9/25/2020 PHY 341/641 Spring 2012 -- Lecture 18 12

b. J=2 b. J=1 M/N b. J=0 b. H 9/25/2020 PHY 341/641 Spring 2012

b. J=2 b. J=1 M/N b. J=0 b. H 9/25/2020 PHY 341/641 Spring 2012 -- Lecture 18 13

Mean field approximation for 1 -dimensional Ising model 9/25/2020 PHY 341/641 Spring 2012 --

Mean field approximation for 1 -dimensional Ising model 9/25/2020 PHY 341/641 Spring 2012 -- Lecture 18 14

Mean field partition function and Free energy: 9/25/2020 PHY 341/641 Spring 2012 -- Lecture

Mean field partition function and Free energy: 9/25/2020 PHY 341/641 Spring 2012 -- Lecture 18 15

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