The thermodynamic functions of an n-component d-dimensional 4 theory are written in the form fi=Ait|- i(1+ai|t|), where t=(T-Tc)Tc. The correction-to-scaling amplitudes ai are calculated to leading order in 1n for 2<d<4, and the universality of their ratios is explicitly shown. The effective exponents i,eff= i-ai |t| violate the thermodynamic scaling laws already at this leading order. The amplitudes ai have singularities (as functions of d) at the dimensionalities dI l=2+4l,l=3,4,5,. Above Tc, the specific heat and the susceptibility correction amplitudes ac+ and a+ are discontinuous at dIl and at dI2l(l2), respectively. Below Tc, the magnetization and the stiffness correction amplitudes are zero, aM=as=0, while ac- diverges at di2l+1(l1) but is continuous at d2l (in particular at d=3). Results are also given for universal ratios among corrections-to-scaling amplitudes for the dependence of thermo-dynamic functions on the magnetization at T=Tc and at a nonzero field.
ASJC Scopus subject areas
- Condensed Matter Physics