29::196 Computational Physics: Assignments  for week  11



Readings: Yevick: pp 217-226; email 3 questions  by Tuesday 11/15/05 NOON.

Optional Readings: Newman and Barkema,  MC methods  in SM , Chapters 1 and 2.

Homework (due Thursday  12/1):

1)  Consider the one-dimensional Ising model with N spins (no magnetic field).
     Calculate the partition function, the average
     energy and the two spin correlation with periodic and free boundary conditions.
      Show that the low temperature expansion and the high-temperature expansion yield the same result.
     Using Mathematica, try to reproduce these results using the Metropolis algorithm
    
2) Consider the quantum hamiltonian H=                ((1/2)*p1^2+(1/2)*x1^2+g*x1^4+(1/2)*p2^2+(1/2)*x2^2+g*x2^4-b*x1*x2;
    with g=>0 and 0<=b<1; Discuss the spectrum in the limits  g->0 or b->0;
    When g=0 AND b=0, show that there is a special degeneracy.
    Calculate numerically the first six energy levels for values of g and b of your choice.

3) Problem 16 in  Chapter 9 of Yevick

4)  Using C++, create an array of  10,000 random numbers homogeneously distributed
     between two values of your choice. Make a good looking histogram of the distribution using
      a class Histogram in a PLOT.h file (as in last week exercise in Ch. 8).
      Assume that the lowest and largest values of  a GIVEN list are not known before the
      histogram is made (do not use the addValue function).
      Follow the general idea of the Mathematica notebook histogram.nb

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