Toward extracting scattering phase shifts from integrated correlation functions. V. Complex <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:math> field mode

In Guo [Toward extracting the scattering phase shift from integrated correlation functions. II. A relativistic lattice field theory model, .] and associated studies, a relativistic finite-volume formalism in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>1</a:mn> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:math> dimensions is proposed to extract infinite-volume scattering phaseshift. It is based on the difference of integrated correlation functions rather than energy spectrum in the finite volume, and can be regarded as complementary to the well-known Lüscher formalism. In the present work, the formalism is further extended into <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mn>3</c:mn> <c:mo>+</c:mo> <c:mn>1</c:mn> </c:math> dimensional spacetime. The aim is to explore and demonstrate the challenges in applying the formalism to more practical settings. Specifically, Monte Carlo simulations of a complex <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi>ϕ</e:mi> <e:mn>4</e:mn> </e:msup> </e:math> relativistic field model are carried out in both <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mn>2</g:mn> <g:mo>+</g:mo> <g:mn>1</g:mn> </g:mrow> </g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mrow> <i:mn>3</i:mn> <i:mo>+</i:mo> <i:mn>1</i:mn> </i:mrow> </i:math> dimensions on lattices of varying sizes, and phaseshifts for the contact interaction are extracted from the formalism using modest computing resources.