# Zeros of the partition function

1. Mar 17, 2008

### mhill

given a partition function

$$Tr[e^{-BH}]$$ or $$Z(B)= \int_{P}dx dp e^{-BH(p,q)}$$

is there any meaning for its zeros ? , i mean what happens in case the partition function Z(B)=0 for some 'B' or temperature $$B=1/kT$$ do these zeros have a meaning ?? thanks

2. Mar 18, 2008

### olgranpappy

what you have written is positive definite so it has no zeros (i.e., is never zero)... assuming beta is real... and assuming H is a true Hamiltonian...