have recently been simplified by a duality relation based on hypergraphs [@zare18] where partition function of a classical spin model defined on a hypergraph $H$ can be written as an inner product of a product state and a CSS state defined on the dual hypergraph $\tilde{H}$. Using the above dual correspondence, concepts from measurement based quantum computation have been used for considering complexity of classical spin models [@Bravyi2007; @Bombin2008]. In particular, concept of completeness in statistical models [@Nest2008; @Vahid2012b; @Cuevas2009; @xu; @Vahid2012; @yahya] and recently universal models [@science; @cub] have emerged in statistical physics which has opened an important window toward a unification in statistical mechanical models.

On the other hand, one of important and well-established problems in statistical mechanics is the existence of thermal phase transition in classical spin models [@pathr]. In this respect and using the dual correspondence between classical spin models and quantum CSS states, one can expect to find an interpretation of phase transition in classical models for quantum CSS states. For example, it has recently been shown that thermal phase transitions in classical spin models are mapped to topological phase transitions in the corresponding CSS models [@zarei19]. Furthermore, the above mapping has led to insights 