Market crashes as second-order phase transitions

We study the behavior of ensemble features of financial markets during crash periods to see if they exhibit the behavior typical for second-order phase transitions. We find that during market crashes the order parameter (defined as the ensemble-average correlation) sharply increases and fluctuations (defined as ensemble volatility) exhibit a spike. In addition, the hysteresis effect is observed for correlations and drawdown (market drop) and a similar effect exists for trading volume and drawdown. These facts point that during crashes the markets not only resemble, but undergo a second-order phase transition. Market phases can be identified on a trading volume vs drawdown diagram as regions with high and low order parameter. While market dynamics has a self-coordinated nature, the two inputs on phase diagram are measurable directly from the markets.