2. 1D Ising model Consider the Ising model in 1D with zero external field. The Ising Hamiltonian in this case is N-1 #=-JΣ σίσί+1, i=1 where σ = ±1, J > 0. In this problem I am asking to plot some graphs. You can use any graphics software, e.g. gnuplot, excel, etc. (a) (b) (c) (d) Calculate the ground-state energy. Calculate the canonical partition function. Calculate the probability that all spins are aligned. Consider the limit N → ∞. Plot this probability versus kBT/J for few values of N, say N = 103 and N = 108. Argue that your result indicates the absence of ordered state at T > 0. Calculate the Helmholtz free energy A, average energy E, heat capacity C, and the entropy. Plot graphs for A/(JN), E/(JN) and C/N vs kBT/J. In few words discuss your results.
2. 1D Ising model Consider the Ising model in 1D with zero external field. The Ising Hamiltonian in this case is N-1 #=-JΣ σίσί+1, i=1 where σ = ±1, J > 0. In this problem I am asking to plot some graphs. You can use any graphics software, e.g. gnuplot, excel, etc. (a) (b) (c) (d) Calculate the ground-state energy. Calculate the canonical partition function. Calculate the probability that all spins are aligned. Consider the limit N → ∞. Plot this probability versus kBT/J for few values of N, say N = 103 and N = 108. Argue that your result indicates the absence of ordered state at T > 0. Calculate the Helmholtz free energy A, average energy E, heat capacity C, and the entropy. Plot graphs for A/(JN), E/(JN) and C/N vs kBT/J. In few words discuss your results.
Related questions
Question
![2. 1D Ising model
Consider the Ising model in 1D with zero external field. The Ising Hamiltonian in this case is
N-1
#=-JΣ σίσί+1,
i=1
where σ = ±1, J > 0. In this problem I am asking to plot some graphs. You can use any graphics
software, e.g. gnuplot, excel, etc.
(a)
(b)
(c)
(d)
Calculate the ground-state energy.
Calculate the canonical partition function.
Calculate the probability that all spins are aligned. Consider the limit N → ∞. Plot
this probability versus kBT/J for few values of N, say N = 103 and N = 108. Argue that your
result indicates the absence of ordered state at T > 0.
Calculate the Helmholtz free energy A, average energy E, heat capacity C, and the
entropy. Plot graphs for A/(JN), E/(JN) and C/N vs kBT/J. In few words discuss your
results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b65ef36-cf51-4f81-80a6-74e205c9e9b1%2F181324ca-a43e-405f-8292-e65b0c3e6798%2Fongu58_processed.png&w=3840&q=75)
Transcribed Image Text:2. 1D Ising model
Consider the Ising model in 1D with zero external field. The Ising Hamiltonian in this case is
N-1
#=-JΣ σίσί+1,
i=1
where σ = ±1, J > 0. In this problem I am asking to plot some graphs. You can use any graphics
software, e.g. gnuplot, excel, etc.
(a)
(b)
(c)
(d)
Calculate the ground-state energy.
Calculate the canonical partition function.
Calculate the probability that all spins are aligned. Consider the limit N → ∞. Plot
this probability versus kBT/J for few values of N, say N = 103 and N = 108. Argue that your
result indicates the absence of ordered state at T > 0.
Calculate the Helmholtz free energy A, average energy E, heat capacity C, and the
entropy. Plot graphs for A/(JN), E/(JN) and C/N vs kBT/J. In few words discuss your
results.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)