At a continuous phase transition, the equilibrium phases meet without a discontinuous change in a first derivative of the appropriate thermodynamic potential. A thermal continuous transition therefore has no latent heat, although heat capacity or another response can be singular.
An ordinary critical transition develops fluctuations over an increasingly large correlation length. For magnetic ordering, the magnetization can emerge continuously while the magnetic susceptibility grows sharply. Critical exponents describe these changes, and universality explains why microscopically different systems can share them. Finite size, finite measurement time and imperfect tuning round the ideal singularity. The description must distinguish such critical behavior from a weakly first-order transition whose small discontinuity happens to be unresolved.
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