(4) Consider a system in equilibrium at temperature T (or ß = 1/kT), which responds to external field H and take different energies: E (0,, 02) = J0,02 - H,0,H – H202H, where J > 0, 4, > 0, µ2 > 0, and 0, = ±1; 02 = ±1. (You are thinking of a system that consist of two spins, in which H is a magnetic field, J is an interaction to make spins anti-parallel, and µ1, µz are magnetic moments. But you don't need to know this (although you saw this in lecture) or quantum mechanics.) (a) Calculate the partition function. (b) Calculate the average (m) of the "magnetization" m = (4,01 + H202)/2. (c) Calculate the “magnetic susceptibility" at zero external field x(#) = (7 (m) ән H=0 and show that high-temperature limit gives Curie's law x(B): B. 2 (d) Evaluate low-temperature limit of x(B), separately for µ1 = H2 and u # µ2-
(4) Consider a system in equilibrium at temperature T (or ß = 1/kT), which responds to external field H and take different energies: E (0,, 02) = J0,02 - H,0,H – H202H, where J > 0, 4, > 0, µ2 > 0, and 0, = ±1; 02 = ±1. (You are thinking of a system that consist of two spins, in which H is a magnetic field, J is an interaction to make spins anti-parallel, and µ1, µz are magnetic moments. But you don't need to know this (although you saw this in lecture) or quantum mechanics.) (a) Calculate the partition function. (b) Calculate the average (m) of the "magnetization" m = (4,01 + H202)/2. (c) Calculate the “magnetic susceptibility" at zero external field x(#) = (7 (m) ән H=0 and show that high-temperature limit gives Curie's law x(B): B. 2 (d) Evaluate low-temperature limit of x(B), separately for µ1 = H2 and u # µ2-
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Transcribed Image Text:(4) Consider a system in equilibrium at temperature T (or B = 1/kT), which responds to external
field H and take different energies:
E(01,02) = J0,02 – H10,H – H202H,
where J > 0, 41 > 0,µ2 > 0, and
01 = ±1; 02 = ±1.
(You are thinking of a system that consist of two spins, in which H is a magnetic field, J is an
interaction to make spins anti-parallel, and µ1, µ2 are magnetic moments. But you don't need to
know this (although you saw this in lecture) or quantum mechanics.)
(a) Calculate the partition function.
(b) Calculate the average (m) of the "magnetization" m = (4,o, + H202)/2.
(c) Calculate the "magnetic susceptibility" at zero external field
x(B) = (m)
H=0
and show that high-temperature limit gives Curie's law
Hi² + Hz?
ß.
2
x(B)
(d) Evaluate low-temperature limit of x(B), separately for µ, = µ2 and µ, # µ2.
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