Study of the Influence of Random Fields on Phase Transitions Using the Example of the Exactly Solvable Model

The influence of random fields on phase transitions in disordered systems has been studied using an exactly solvable model as an example. The value of the critical dimension \(d_{cr}=6\) $d_{\mathit{cr}}=6$ has been found, and the existence of a dimensional shift \(d'=d-2\) $d^{\prime }=d-2$ has been established, which transforms the value of the critical indices of systems with random fields into the value of the critical indices of pure systems of the corresponding model. The phenomenological generalization of the model has been made taking into account the additional critical index \(\theta\) $\theta$ associated with violation of scale invariance.