Partition function zeros and finite size scaling for polymer adsorption

Abstract

The zeros of the canonical partition functions for a flexible polymer chain tethered to an attractive flat surface are computed for chains up to length N = 1536. We use a bond-fluctuation model for the polymer and obtain the density of states for the tethered chain by Wang-Landau sampling. The partition function zeros in the complex e(β)-plane are symmetric about the real axis and densest in a boundary region that has the shape of a nearly closed circle, centered at the origin, terminated by two flaring tails. This structure defines a root-free zone about the positive real axis and follows Yang-Lee theory. As the chain length increases, the base of each tail moves toward the real axis, converging on the phase-transition point in the thermodynamic limit. We apply finite-size scaling theory of partition-function zeros and show that the crossover exponent defined through the leading zero is identical to the standard polymer adsorption crossover exponent ϕ. Scaling analysis of the leading zeros locates the polymer adsorption transition in the thermodynamic (N → ∞) limit at reduced temperature Tc (*)=1.027(3) [βc=1/Tc (*)=0.974(3)] with crossover exponent ϕ = 0.515(25). Critical exponents for the order parameter and specific heat are determined to be β̃=0.97(5) and α = 0.03(4), respectively. A universal scaling function for the average number of surface contacts is also constructed.

Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model

“…For the lengths obtained by FlatPERM we can see that the estimates extrapolate well to the previously found value, for the ISAT model for large enough N . The points are fitted following Taylor and Luettmer-Strathmann [ 30 ], who fitted the real part of the zero as a polynomial of the imaginary part. As the imaginary part goes to zero as the length of the walk goes to zero, the asymptotic estimate is given by the constant part of the constructed polynomial.…”

Subphase transitions in first-order aggregation processes

“…Due to the averaging process involved in the calculation of canonical quantities such as the ensemble energy or the heat capacity, specific features of structural transitions and phase properties are often lost [3]. This is remedied in more general approaches such as the Fisher partition zeros [55][56][57][58], or the microcanonical inflection-point analysis [59,60].…”

Confinement effects upon the separation of structural transitions in linear systems with restricted bond fluctuation ranges

“…The intricate impact of finite-size effects on the thermodynamic phase behavior requires careful statistical analyses beyond conventional canonical methods that typically do not allow for a unique identification of transition points in finite systems [2,8]. On the contrary, general methods such as analyses of inflec-tion points in the microcanonical temperature curve [67], which is based on microcanonical thermodynamics [68], autocorrelation times [69], and Fisher partition function zeros [70] have been employed successfully recently [71][72][73].…”