Financial crises are known as crashes that result in a sudden loss of value of financial assets in large part and they continue to occur from time to time surprisingly. In order to discover features of the financial network, the pairwise interaction of stocks has been considered in many research, but the existence of the strong correlation of stocks and their collective behavior in crisis made us address higher-order interactions. Hence, in this study, we investigate financial networks by triplet interaction in the framework of balance theory. Due to detecting the contribution of higher-order interactions in understanding the complex behavior of stocks we take the advantage of the orders parameters of the higher-order interactions. Looking at real data of financial market obtained from S&P500 through the lens of balance theory for the quest of network structure in different periods of time near and far from crisis reveals the existence of a structural difference of the network that corresponds to different periods of time. Here, we address two well-known crises the Great regression ( 2008) and the Covid-19 recession (2020). Results show an ordered structure forms on-crisis in the financial network while stocks behave independently far from a crisis. The formation of the ordered structure of stocks in crisis makes the network resistant against disorder. The resistance of the ordered structure against applying a disorder (temperature) can measure the crisis strength and determine the temperature at which the network transits. There is a critical temperature, T c , in the language of statistical mechanics and mean-field approach which above, the ordered structure destroys abruptly and a first-order phase transition occurs. The stronger the crisis, the higher the critical temperature.

In financial crises, assets see a deep loss of value, and the financial markets experience liquidity shortages. Although they are not uncommon, they may cause by multiple contributing factors which makes them hard to study. To discover features of the financial network, the pairwise interaction of stocks has been considered in many pieces of research, but the existence of the strong correlation between stocks and their collective behavior in crisis made us address higher-order interactions. Hence, in this study, we investigate financial networks by triplet interaction in the framework of balance theory. Due to detecting the contribution of higher-order interactions in understanding the complex behavior of stocks we take the advantage of the order parameter of the higher-order interactions. Looking at real data of the financial market obtained from S&P500 index(SPX) through the lens of balance theory for the quest of network structure in different periods (on and off-crisis) faces us with the existence of a structural difference of networks corresponding to the periods. Addressing two well-known crises the Great regression (2008) and the Covid-19 recession (2020), our results show an ordered structure forms in the on-crisis period in the financial network while stocks behave independently far from a crisis. The formation of the ordered structure of stocks in crisis makes the network more resilient to disorder (thermal fluctuations). The resistance of the ordered structure against applying the disorder measure the crisis strength and determine the temperature at which the network transits. There is a critical temperature, Tc, in the language of statistical mechanics and mean-field approach which above, the ordered structure destroys abruptly and a first-order phase transition occurs. The stronger the crisis, the higher the critical temperature.