  In this paper, we consider an exponential scalar auxiliary variable (E-SAV)
approach to obtain energy stable schemes for a class of phase field models.
This novel auxiliary variable method based on exponential form of nonlinear
free energy potential is more effective and applicable than the traditional SAV
method which is very popular to construct energy stable schemes. The first
contribution is that the auxiliary variable without square root removes the
bounded from below restriction of the nonlinear free energy potential. Then, we
prove the unconditional energy stability for the semi-discrete schemes
carefully and rigorously. Another contribution is that we can discrete the
auxiliary variable combined with the nonlinear term totally explicitly. Such
modification is very efficient for fast calculation. Furthermore, the positive
property of $r$ can be guaranteed which is very important and reasonable for
the models' equivalence. Besides, for complex phase field models with two or
more unknown variables and nonlinear terms, we construct a multiple E-SAV
(ME-SAV) approach to enhance the applicability of the proposed E-SAV approach.
A comparative study of classical SAV and E-SAV approaches is considered to show
the accuracy and efficiency. Finally, we present various 2D numerical
simulations to demonstrate the stability and accuracy.
