Folding of the triangular lattice in a discrete three-dimensional space: density-matrix renormalization-group study

Area of Science:

• * Computational physics
• * Polymer physics
• * Statistical mechanics

Background:

• * Discrete folding models, like those for phantom polymerized membranes, are simplified theoretical constructs.
• * Previous analyses using the hexagon approximation of the cluster variation method (CVM) had limitations in accuracy and computational scope.
• * Transfer-matrix calculations were restricted to small strip widths (L≤6), hindering reliable extrapolation to the thermodynamic limit.

Purpose of the Study:

• * To overcome the limitations of previous methods for analyzing discrete folding.
• * To accurately investigate the crumpling transition of triangular lattices in a discrete 3D space.
• * To provide reliable extrapolations to the thermodynamic limit by enabling the treatment of larger system sizes.

Main Methods:

• * Employed the density-matrix renormalization group (DMRG) technique.
• * Successfully treated significantly larger strip widths (up to L=29) compared to prior studies.
• * Enabled reliable extrapolations to the thermodynamic limit.

Main Results:

• * Observed an onset of a discontinuous crumpling transition.
• * The calculated latent heat was substantially larger than CVM estimates and even exceeded that of 2D folding.
• * Folding entropy was found to be within previously established analytical bounds.

Conclusions:

• * The discontinuous nature of the crumpling transition is enhanced by increasing the embedding space dimensions (3D vs. 2D).
• * DMRG provides a more accurate and scalable approach for studying discrete folding phenomena.
• * The findings challenge naive expectations regarding the effect of dimensionality on crumpling transitions.