GATE Exam > GATE Questions > Consider a system of two ising spin S1and S2t...
Start Learning for Free
Consider a system of two ising spin S1 and S2 taking value ±1 with interaction energy ∈ = -JS1S2 in thermal equilibrium at temperature T. The partition function of the system in the limit T → ∞ is ______.
Correct answer is '4'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Consider a system of two ising spin S1and S2taking value ±1 wit...
Most Upvoted Answer
Consider a system of two ising spin S1and S2taking value ±1 wit...
+1 or -1. The energy of the system is given by:
E = -J(S1S2)
where J is a constant that represents the strength of the interaction between the spins.
The possible configurations of the system are:
S1 = +1, S2 = +1: energy E = -J
S1 = +1, S2 = -1: energy E = J
S1 = -1, S2 = +1: energy E = J
S1 = -1, S2 = -1: energy E = -J
The probability of each configuration depends on the temperature of the system and can be calculated using the Boltzmann distribution:
P(S1,S2) = exp(-E(S1,S2)/kT) / Z
where k is the Boltzmann constant, T is the temperature of the system, and Z is the partition function:
Z = ∑ exp(-E(S1,S2)/kT)
The partition function is the sum of the probabilities of all possible configurations and ensures that the probabilities are normalized.
The average value of each spin can be calculated as:
= ∑ S1P(S1,S2)
= ∑ S2P(S1,S2)
The correlation between the spins can be calculated as:
C = -
where is the average value of the product of the spins.
At high temperatures, when kT >> J, the Boltzmann distribution becomes nearly flat and all configurations are equally probable. In this case, the average value of each spin is zero and the correlation between the spins is also zero.
At low temperatures, when kT < j,="" the="" boltzmann="" distribution="" is="" dominated="" by="" the="" lowest="" energy="" configuration,="" where="" the="" spins="" are="" aligned.="" in="" this="" case,="" the="" average="" value="" of="" each="" spin="" is="" either="" +1="" or="" -1,="" depending="" on="" the="" sign="" of="" j,="" and="" the="" correlation="" between="" the="" spins="" is="" positive.="" j,="" the="" boltzmann="" distribution="" is="" dominated="" by="" the="" lowest="" energy="" configuration,="" where="" the="" spins="" are="" aligned.="" in="" this="" case,="" the="" average="" value="" of="" each="" spin="" is="" either="" +1="" or="" -1,="" depending="" on="" the="" sign="" of="" j,="" and="" the="" correlation="" between="" the="" spins="" is="" />
E = -J(S1S2)
where J is a constant that represents the strength of the interaction between the spins.
The possible configurations of the system are:
S1 = +1, S2 = +1: energy E = -J
S1 = +1, S2 = -1: energy E = J
S1 = -1, S2 = +1: energy E = J
S1 = -1, S2 = -1: energy E = -J
The probability of each configuration depends on the temperature of the system and can be calculated using the Boltzmann distribution:
P(S1,S2) = exp(-E(S1,S2)/kT) / Z
where k is the Boltzmann constant, T is the temperature of the system, and Z is the partition function:
Z = ∑ exp(-E(S1,S2)/kT)
The partition function is the sum of the probabilities of all possible configurations and ensures that the probabilities are normalized.
The average value of each spin can be calculated as:
The correlation between the spins can be calculated as:
C =
where
At high temperatures, when kT >> J, the Boltzmann distribution becomes nearly flat and all configurations are equally probable. In this case, the average value of each spin is zero and the correlation between the spins is also zero.
At low temperatures, when kT < j,="" the="" boltzmann="" distribution="" is="" dominated="" by="" the="" lowest="" energy="" configuration,="" where="" the="" spins="" are="" aligned.="" in="" this="" case,="" the="" average="" value="" of="" each="" spin="" is="" either="" +1="" or="" -1,="" depending="" on="" the="" sign="" of="" j,="" and="" the="" correlation="" between="" the="" spins="" is="" positive.="" j,="" the="" boltzmann="" distribution="" is="" dominated="" by="" the="" lowest="" energy="" configuration,="" where="" the="" spins="" are="" aligned.="" in="" this="" case,="" the="" average="" value="" of="" each="" spin="" is="" either="" +1="" or="" -1,="" depending="" on="" the="" sign="" of="" j,="" and="" the="" correlation="" between="" the="" spins="" is="" />
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
Consider a system of two ising spin S1and S2taking value ±1 with interaction energy ∈ = -JS1S2 in thermal equilibrium at temperature T. The partition function of the system in the limit T → ∞ is ______.Correct answer is '4'. Can you explain this answer?
Question Description
Consider a system of two ising spin S1and S2taking value ±1 with interaction energy ∈ = -JS1S2 in thermal equilibrium at temperature T. The partition function of the system in the limit T → ∞ is ______.Correct answer is '4'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider a system of two ising spin S1and S2taking value ±1 with interaction energy ∈ = -JS1S2 in thermal equilibrium at temperature T. The partition function of the system in the limit T → ∞ is ______.Correct answer is '4'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a system of two ising spin S1and S2taking value ±1 with interaction energy ∈ = -JS1S2 in thermal equilibrium at temperature T. The partition function of the system in the limit T → ∞ is ______.Correct answer is '4'. Can you explain this answer?.
Consider a system of two ising spin S1and S2taking value ±1 with interaction energy ∈ = -JS1S2 in thermal equilibrium at temperature T. The partition function of the system in the limit T → ∞ is ______.Correct answer is '4'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider a system of two ising spin S1and S2taking value ±1 with interaction energy ∈ = -JS1S2 in thermal equilibrium at temperature T. The partition function of the system in the limit T → ∞ is ______.Correct answer is '4'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a system of two ising spin S1and S2taking value ±1 with interaction energy ∈ = -JS1S2 in thermal equilibrium at temperature T. The partition function of the system in the limit T → ∞ is ______.Correct answer is '4'. Can you explain this answer?.
Solutions for Consider a system of two ising spin S1and S2taking value ±1 with interaction energy ∈ = -JS1S2 in thermal equilibrium at temperature T. The partition function of the system in the limit T → ∞ is ______.Correct answer is '4'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of Consider a system of two ising spin S1and S2taking value ±1 with interaction energy ∈ = -JS1S2 in thermal equilibrium at temperature T. The partition function of the system in the limit T → ∞ is ______.Correct answer is '4'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Consider a system of two ising spin S1and S2taking value ±1 with interaction energy ∈ = -JS1S2 in thermal equilibrium at temperature T. The partition function of the system in the limit T → ∞ is ______.Correct answer is '4'. Can you explain this answer?, a detailed solution for Consider a system of two ising spin S1and S2taking value ±1 with interaction energy ∈ = -JS1S2 in thermal equilibrium at temperature T. The partition function of the system in the limit T → ∞ is ______.Correct answer is '4'. Can you explain this answer? has been provided alongside types of Consider a system of two ising spin S1and S2taking value ±1 with interaction energy ∈ = -JS1S2 in thermal equilibrium at temperature T. The partition function of the system in the limit T → ∞ is ______.Correct answer is '4'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider a system of two ising spin S1and S2taking value ±1 with interaction energy ∈ = -JS1S2 in thermal equilibrium at temperature T. The partition function of the system in the limit T → ∞ is ______.Correct answer is '4'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup