GL Market Phase Transition Model¶
RTSG × Ginzburg-Landau · S&P 500 · Live
Current State (2026-03-23)¶
| Parameter | Value | Interpretation |
|---|---|---|
| SPY Close | $655.38 | |
| Phase | DISORDERED | Mean-reverting regime |
| α (stability) | 1.30 | Strong mean reversion |
| Volatility | 11.9% | Low |
| Trend (W) | -3.76% | Below 20-day MA |
| Susceptibility | 0.77 | Low (market robust) |
| Hurst exponent | 0.71 | Persistent (trending) |
Regime: 🔵 MEAN REVERSION — market is stabilizing after recent selloff
The Model¶
The GL action on market state \(W\):
\[S[W] = \int \left( |\partial_t W|^2 + \alpha |W|^2 + \frac{\beta}{2} |W|^4 \right) dt\]
Where: - \(W\) = trend strength (deviation from moving average) - \(\alpha\) = stability parameter (estimated from return autocorrelation) - \(\beta\) = nonlinear stabilization (estimated from excess kurtosis)
Phase Interpretation¶
| α value | Phase | Market behavior | Physics analogy |
|---|---|---|---|
| α > 0 | DISORDERED | Mean-reverting, prices return to fair value | Paramagnet (spins random) |
| α ≈ 0 | CRITICAL | Phase transition, susceptibility diverges, fragile | Critical point (Curie temperature) |
| α < 0 | ORDERED | Trend-following, momentum, bubbles/crashes | Ferromagnet (spins aligned) |
Key Observables¶
- Susceptibility \(\chi = 1/|\alpha|\): Diverges at the critical point. High susceptibility = market responds disproportionately to small shocks.
- Relaxation time \(\tau = 1/\sqrt{|\alpha|}\): How long disturbances take to decay. Diverges at critical point.
- Condensate \(|W_0| = \sqrt{-\alpha/\beta}\): Equilibrium trend strength in the ordered phase.
- Hurst exponent \(H\): \(H > 0.5\) = persistent (trends continue), \(H < 0.5\) = anti-persistent (trends reverse), \(H = 0.5\) = random walk.
Recent Phase Transitions¶
| Date | Direction | What happened |
|---|---|---|
| 2025-04-10 | → DISORDERED | Market stabilized after Q1 momentum |
| 2025-07-17 | → ORDERED | Brief momentum spike |
| 2025-07-18 | → DISORDERED | Immediate reversion |
| 2026-01-07 | → ORDERED | New Year momentum regime |
| 2026-02-23 | → DISORDERED | Current mean-reverting regime |
Connection to RTSG¶
The Boltzmann-McFadden isomorphism maps:
| Physics | Markets |
|---|---|
| Energy | Negative utility |
| Temperature \(T\) | Inverse risk aversion \(1/\beta\) |
| Order parameter \(W\) | Trend strength |
| Phase transition | Crash / bubble |
| Landauer floor \(kT\ln 2\) | Minimum cost per trading decision |
| Susceptibility \(\chi\) | Market fragility |
The complexification functor says markets spiral — same seasonal patterns at different altitudes. Monday isn't last Monday.
Implementation¶
- Data source: yfinance (S&P 500 SPY ETF)
- Window: 60-day rolling estimation
- α estimation: Negative autocorrelation × 10 (positive autocorr = momentum → negative α)
- β estimation: Excess kurtosis / 5 (heavy tails = strong nonlinear stabilization)
- Dashboard: React + Recharts, live at artifacts
Literature¶
- Bouchaud, Bonamy, "Financial markets and the phase transition between water and steam" (ScienceDirect 2022) — directly measures GL coefficients
- Fry, "Endogenous and Endogenous Crashes as Phase Transitions" (2012) — market crashes as first-order transitions
- Sornette, "Why Stock Markets Crash" (2003) — log-periodic power law
Research tool only. Not investment advice. RTSG BuildNet · Jean-Paul Niko · smarthub.my