Register to reply

Partition function for hard spheres on a lattice

by Yoran91
Tags: function, lattice, partition, spheres
Share this thread:
Mar4-13, 01:35 PM
P: 37
Hi everyone,

I'm reading some lecture notes on statistical physics and thermodynamics and I'm stuck at an expression for a partition function which I really don't understand.

The chapter is on mean field theory and the discussion is about hard spheres on a lattice. The interaction of the hard sphere is [itex]\beta U = \infty[/itex] if [itex]r<\sigma[/itex] and [itex]\beta U = 0[/itex] if [itex]r>\sigma [/itex] as usual, where [itex]\sigma[/itex] is the diameter of the spheres.

Now it's said that a single hard sphere is treated exactly and the other spheres are located at their 'ideal' lattice positions. This supposedly leads to [itex]Z_N=\prod_{i=1}^N V_i[/itex] where [itex]V_i[/itex] is the free volume in which the center of mass of particle i can move.

I really don't see this. I'm expecting an [itex]h^3[/itex] or [itex]\Lambda ^3[/itex] to appear somewhere, obtained by integrating over the momenta of such a sphere, but it isn't there. Why is this the partition function?
Phys.Org News Partner Physics news on
Step lightly: All-optical transistor triggered by single photon promises advances in quantum applications
The unifying framework of symmetry reveals properties of a broad range of physical systems
What time is it in the universe?

Register to reply

Related Discussions
Collision between hard spheres General Physics 12
Partition function to find expected occupancy of a lattice defect Advanced Physics Homework 0
K*Lucas_n + 1 is a prime of Lucas Number Index (a Lattice/Partition # Relationship?) Linear & Abstract Algebra 0
Format hard drive / delete NTFS partition (Windows XP) Computing & Technology 6
Increasing capacity of hard drive partition Computing & Technology 17