Monte Carlo evaluation of the continuum limit of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>ϕ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>12</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:math>

Abstract

Abstract We study canonical and affine versions of non-renormalizable Euclidean classical scalar field-theory with twelfth-order power–law interactions on three dimensional lattices through the Monte Carlo method. We show that while the canonical version of the model turns out to approach a ‘free-theory’ in the continuum limit, the affine version is perfectly well defined as an interaction model.

Topics & Concepts