Reference no: EM131347760
A one-dimensional, spin-one model of magnetism
Consider a one-dimensional macroscopic model with spin-one quantum mechanical magnetic moments located on each of N sites. The Hamiltonian is
where each σj takes on the values -1, 0, or +1, J is an exchange interaction parameter, h is a magnetic field, and D is a parameter representing a ‘crystal field'. The entire system is in contact with a thermal reservoir at temperature T.
1. Write down a formal expression for the partition function of this system. You do not have to evaluate any sums or integrals that appear in your expression for this part of the problem.
2. For general values of the parameters, derive a formal expression for the quantity
in terms of a derivative of the partition function with respect to an appropriate parameter.
3. For J = 0, but arbitrary values of h and D, calculate the partition function for this system.
4. For J = 0, but arbitrary values of h and D, calculate the free energy of this system.
5. For J = 0 and h = 0, calculate the entropy of this system.
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Monte carlo simulations of a two-dimensional ising model
: Do a simulation of a 32 × 32 lattice with negative temperature, and print out the spins at the end of the run. Begin with the spins in a random state (T = ∞), and simulate for 100 sweeps at T = -1.0. What do you see?
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Types of project management approaches
: Provide description of which types of project management approaches are used by your HSO or an HSO with which you are familiar. Then, explain the strengths and weaknesses of using these types of project management approaches in contributing value ..
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Identifies and describe the strong points of the managers
: Mgmt 499- Assesses how the overall management teams perform in terms of the four functions of management. Identifies and explains the strong points of the managers. Identifies and explains areas in which improvements are needed.
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Specific strengths of the process from perspectives
: What are your thoughts about the strategic planning process? How well is it working? What are specific strengths of the process from your perspectives? Have you encountered any barriers or difficulties to overcome?
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Calculate the partition function for this system
: Write down a formal expression for the partition function of this system. You do not have to evaluate any sums or integrals that appear in your expression for this part of the problem.
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Project management overview
: Use the characteristics of a project to differentiate it from operations work.- Describe which characteristics of project success you think are the most important, and why.
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What way knowledge about yourself may impact your ability
: Now reflect forward and consider in what ways this new knowledge about yourself may impact your ability to be an effective leader as your professional career moves forward.
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Compute the price of coupon bond
: Compute the price of a 5.5 percent coupon bond with 15 years left to maturity and a market interest rate of 8.8 percent.
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Constraint modeling the situation
: Write a constraint modeling the situation in which at least 2of the project from 1, 2, 4, and 6 must be selected. Write a constraint modeling the situation in which only 2of the projects from 1, 2, 3, and 4 must be selected.
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