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Abstract
We investigate the non-perturbative features of $\phi^4_2$ theory in two dimensions, using Monte Carlo lattice methods. In particular we determine the ratio $f_0 \equiv g/\mu^2$, where g is the unrenormalised coupling, in the infinite volume and continuum limit. Our final result is $f_0$ = 11.055(14).
Highlights
Φ4 theory plays an important role in quantum field theory as it represents for example an extremely simplified model for the Higgs sector of the Standard Model
We investigate the nonperturbative features of φ4 theory in two dimensions, using Monte Carlo lattice methods
In D 1⁄4 2 dimensions the theory is super-renormalizable: the coupling constant g has positive mass dimensions 1⁄2g 1⁄4 1⁄2μ20, where μ0 is the mass parameter of the theory; this means that the ratio f ≡ g=μ2, where μ2 is a renormalized squared mass in some given renormalization scheme, is the only physically relevant dimensionless parameter we have to consider
Summary
Φ4 theory plays an important role in quantum field theory as it represents for example an extremely simplified model for the Higgs sector of the Standard Model. In this paper we determine the value of f ≡ g=μ2 at the critical point, that is the value of f computed in the limit in which both g and μ2 go to zero. We follow the renormalization scheme used in [1,2], adopting the simulation technique introduced in [3,4], namely the worm algorithm, and we compute the ratio g=μ2 using the same strategy implemented in [5]; we present an improvement in the determination of the critical value f0, obtained thanks to the gradient flow [6], a technique that allows us to reach smaller values of the coupling g with respect to our previous work [5]. In the end we will compare our results with our previous determination of the same quantity, and we will draw some conclusions
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