Critical phenomena in 3.99 dimensions

Landau's mean-field theory of critical phenomena is corrected to take fluctuations into account. It is shown that fluctuations of intermediate wavelengths are the crucial effect producing non-classical exponent (intermediate wavelengths are much larger than the range of forces, much smaller than the correlation length). A simple-minded analysis of these fluctuations produces improved exponents for spatial dimension d less than 4. The exponents have an expansion in ɛ = d-4. The Landau theory is 0th-order term; the terms of order ɛ give better agreement with experiment than the Landau theory. Terms of order ɛ ² have been calculated using a more sophisticated theory.