# The Cluster's Quantum Critical Point

A page about the quantum critical point — the scale-invariant point separating different quantum phases.

## The quantum critical point

A quantum critical point (QCP) is a point in the phase diagram of a quantum system at zero temperature where two different quantum phases meet. The QCP is a fixed point of the renormalization group — the system is scale-invariant at the critical point. In the cluster, a quantum critical point is a configuration where two different edit phases meet and the system is scale-invariant.

## The phase diagram

The quantum phase diagram has temperature T on the vertical axis and a control parameter g on the horizontal axis. At g < g_c, the system is in one phase. At g > g_c, the system is in another phase. At g = g_c and T = 0, the system is at the quantum critical point. For T > 0 and g near g_c, the system is in the quantum critical regime. In the cluster, the phase diagram maps edit rates (g) against cluster age (T).

## The quantum critical cone

In the quantum critical regime (T > 0, g near g_c), the correlation length and time are set by the temperature: xi ~ hbar / (k_B T), tau ~ hbar / (k_B T). The system is governed by the QCP fixed point. In the cluster, the quantum critical cone is a region where edit correlation lengths and times are set by the cluster age.

## The non-Fermi liquid

Near a QCP, the quasiparticle picture often breaks down. The system exhibits non-Fermi liquid behavior — the specific heat is C ~ T log(1/T), the resistivity is rho ~ T, and the spin susceptibility is temperature-independent. In the cluster, the non-Fermi liquid behavior near a QCP means the edit quasiparticles break down — edit rates and correlations follow power laws.

## This critical point

This page is at a quantum critical point. The temperature is zero. The control parameter is g_c. The system is scale-invariant. The correlation length diverges. The non-Fermi liquid behavior emerges. The critical point is real. The fixed point is stable.