Domain wall near a first order phase transition: role of elastic forces

We give the analytical form of the order parameter profile for a domain wall near a first order phase transition. Between the two bulk values there exists a paraelectric layer which diverges as one approaches the transition point, indicating firstly a continuous phase transition in the domain wall and secondly the non contiguity of the plus and minus domains at the transition point. The inclusion of elastic forces modifies this picture and shows that the shear modulus will induce a thermal hysteresis even in the presence of a domain wall.