Effects of boundary conditions and gradient flow in 1+1 dimensional lattice $\phi^4$ theory
A. Harindranath, Jyotirmoy Maiti
TL;DR
This paper investigates how boundary conditions and gradient flow influence the phase transition, mass extraction, and boundary artifacts in 1+1 dimensional lattice theory, highlighting the importance of finite volume analysis.
Contribution
It provides a detailed comparison of open and periodic boundary conditions and their effects on phase transition points and mass measurements in lattice theory.
Findings
Open boundary conditions shift the phase transition point to lower coupling values.
Boundary artifacts dominate in the critical region when using open boundaries.
Finite volume effects are significant and require detailed analysis in the critical region.
Abstract
In this work we study the effects of gradient flow and open boundary condition in the temporal direction in 1+1 dimensional lattice theory. Simulations are performed with periodic (PBC) and open (OPEN) boundary conditions in the temporal direction. The Effects of gradient flow and open boundary on the field and the susceptibility are studied in detail along with the finite size scaling analysis. In both cases, at a given volume, the phase transition point is shifted towards a lower value of lattice coupling for fixed in the case of OPEN as compared to PBC with this shift found to be diminishing as volume increases. We compare and contrast the extraction of the boson mass from the two point function (PBC) and the one point function (OPEN) as the coupling, starting from moderate values, approaches the critical value corresponding to the vanishing of the…
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