Properties of phase transitions of higher order
  There is only limited experimental evidence for the existence in nature of phase transitions of Ehrenfest order greater than two. However, there is no physical reason for their non-existence, and such transitions certainly exist in a number of theoretical models in statistical physics and lattice field theory. Here, higher-order transitions are analysed through the medium of partition function zeros. Results concerning the distributions of zeros are derived as are scaling relations between some of the critical exponents. 
W. Janke, D.A. Johnston and R. Kenna