Phase Transition: Potts Model
Q-state generalization of Ising — from continuous to first-order phase transitions
Parameters
States Q:
3
continuous
Temperature T:
1.0
Sweeps/frame:
5
Reset (Random)
Set Cold (Ordered)
0.00
Order param
0.00
Energy/site
0.00
Specific heat
Critical temperatures (2D Potts):
T
c
= 1/ln(1+√Q)
1.14
T
c
(exact)
0.88
T/T
c
Potts model:
each site takes one of Q states. J=+1 (ferromagnetic).
H = −J Σ δ(σᵢ,σⱼ) over neighbors
Q ≤ 4:
continuous (second-order) transition — diverging correlation length, power-law scaling
Q > 4:
first-order — discontinuous jump in order parameter at T
c
, latent heat
Watch the order parameter
sharpen
as Q increases. The chart shows M(T) history.