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In this work we study the effects of gradient flow and open boundarycondition in the temporal direction in 1+1 dimensional lattice $\phi^4$ theory.Simulations are performed with periodic (PBC) and open (OPEN) boundaryconditions in the temporal direction. The Effects of gradient flow and openboundary on the field $\phi$ and the susceptibility are studied in detail alongwith the finite size scaling analysis. In both cases, at a given volume, thephase transition point is shifted towards a lower value of lattice coupling$\lambda_0$ for fixed $m_0^2$ in the case of OPEN as compared to PBC with thisshift found to be diminishing as volume increases. We compare and contrast theextraction of the boson mass from the two point function (PBC) and the onepoint function (OPEN) as the coupling, starting from moderate values,approaches the critical value corresponding to the vanishing of the mass gap.In the critical region, boundary artifacts become dominant in the latter. Ourstudies point towards the need for a detailed finite volume (scaling) analysisof the effects of OPEN in the critical region.

Effects of boundary conditions and gradient flow in 1+1 dimensional lattice $\phi^4$ theory