Partition function zeros and finite size scaling for polymer adsorption

2014 ◽  
Vol 141 (20) ◽  
pp. 204906 ◽  
Author(s):  
Mark P. Taylor ◽  
Jutta Luettmer-Strathmann
Keyword(s):  
Partition Function ◽  
Finite Size ◽  
Polymer Adsorption ◽  
Finite Size Scaling ◽  
Partition Function Zeros ◽  
Size Scaling ◽  
Function Zeros

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

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 153
Author(s):  
Damien Foster ◽  
Ralph Kenna ◽  
Claire Pinettes
Keyword(s):  
Phase Transitions ◽  
Partition Function ◽  
Critical Behavior ◽  
Finite Size ◽  
The Self ◽  
Partition Function Zeros ◽  
Adsorption Transition ◽  
Function Zeros ◽  
Complex Zeros ◽  
Self Avoiding Walk

The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. The finite-size behavior of the zeros is used to estimate the location of phase transitions: the collapse transition in the bulk and the adsorption transition in the presence of a surface. The bulk and surface cross-over exponents, ϕ and ϕ S , are estimated from the scaling behavior of the leading partition function zeros.

scholarly journals Corrections to finite-size scaling in the 3D Ising model based on nonperturbative approaches and Monte Carlo simulations

2017 ◽  
Vol 28 (04) ◽  
pp. 1750044 ◽  
Author(s):  
J. Kaupužs ◽  
R. V. N. Melnik ◽  
J. Rimšāns
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Finite Size ◽  
Scaling Exponent ◽  
Finite Size Scaling ◽  
Corrections To Scaling ◽  
Partition Function Zeros ◽  
Susceptibility Data ◽  
Size Scaling ◽  
3D Ising Model

Corrections to scaling in the 3D Ising model are studied based on nonperturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes [Formula: see text]. Analytical arguments show the existence of corrections with the exponent [Formula: see text], the leading correction-to-scaling exponent being [Formula: see text]. A numerical estimation of [Formula: see text] from the susceptibility data within [Formula: see text] yields [Formula: see text], in agreement with this statement. We reconsider the MC estimation of [Formula: see text] from smaller lattice sizes, [Formula: see text], using different finite-size scaling methods, and show that these sizes are still too small, since no convergence to the same result is observed. In particular, estimates ranging from [Formula: see text] to [Formula: see text] are obtained, using MC data for thermodynamic average quantities, as well as for partition function zeros. However, a trend toward smaller [Formula: see text] values is observed in one of these cases in a refined estimation from extended data up to [Formula: see text]. We discuss the influence of [Formula: see text] on the estimation of critical exponents [Formula: see text] and [Formula: see text].

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