Effect of external field on thermodynamics of the free-fermion model

The effect of external field on the phase transition is studied in a continuous version of the free-fermion dislocationless model. The phase diagram and the values of indices δ=∞, β=+0, γ=3/2 are obtained as well as the explicit expression for the free energy in the strong field limit. Comparison with the six-vertex model is given. While zero-field scaling and the indices δ and β coincide for both the models indicating that they are of the same universality class, the other characteristics, i.e. the value of γ, the phase diagram, and the scaling function are rather different. This <> is the result of the fact that the external field breaks the symmetry of the above models in (sufficiently) different ways. The possibility of experimental observation of the scaling formulas obtained here in two-dimensional crystals undergoing incommensurate phase transition is discussed