= Solution
<Universality> means that systems with different microscopic interactions can have the same asymptotic critical behaviour. Under <renormalization-group flow>, irrelevant microscopic differences shrink, and systems whose critical flows approach the same <renormalization-group fixed point> belong to one <universality class>. Important determinants are spatial dimension, order-parameter <symmetry> and number of components, the range of interactions and any additional relevant constraints. Microscopic <Bravais lattice> shape alone does not normally change the short-range scalar <universality class>.
<Critical exponents>, properly normalized scaling functions and certain dimensionless amplitude ratios are universal within a <universality class>. For example, the <universal specific-heat amplitude ratio> compares the two singular amplitudes above and below the transition, canceling their common normalization factors. Scaling functions require choices of thermal, field and length metric factors before comparisons between microscopic systems make sense. The <critical temperature>, critical field, <Bravais lattice> spacing, individual correlation-length and <magnetic susceptibility> amplitudes, and analytic free-energy backgrounds are not generally universal. Thus two models can share <critical exponents> without sharing their transition <temperature> or the absolute size of their response.
Back to article page
