Phase transitions and finite-size scaling

[Pages:23]Phase transitions and finite-size scaling

? Critical slowing down and "cluster methods". ? Theory of phase transitions/ "Renormalization Group" ? Finite-size scaling

Detailed treatment: "Lectures on Phase Transitions and the Renormalization Group" Nigel Goldenfeld (UIUC).

Atomic Scale Simulation

1

The Ising Model

? Suppose we have a lattice, with L2 lattice sites and connections between them. (e.g. a square lattice).

? On each lattice site, is a single spin

variable: si = ?1. ? With mag. field h, energy is:

N

H = - hs - Js s

i

ij

i=1

(i, j)

? J is the coupling between

Z = e-H

nearest neighbors (i,j)

si = ?1

? J>0 ferromagnetic

? J ................
................

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