Strong Disorder Fixed Point in Absorbing-State Phase Transitions

The effect of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class is studied by a strong disorder renormalization group approach and by density matrix renormalization group calculations. We show that for sufficiently strong disorder the critical behavior is controlled by a strong disorder fixed point and in one dimension the critical exponents are conjectured to be exact: $\beta =(3-\sqrt{5})/2$ and ${\nu }_{\perp }=2$. For disorder strengths outside the attractive region of this fixed point, disorder dependent critical exponents are detected. Existing numerical results in two dimensions can be interpreted within a similar scenario.

Figure 1

Schematic phase diagram of the random contact process as a function of $A$ and $R$ (see text). The inactive and active phases are separated by a phase transition line, along which the critical exponents are $R$ dependent for weaker disorder (WD, $R\le R_c$), or are determined by a strong disorder fixed point at $R=\infty$, for strong disorder (SD, $R>R_c$).

Figure 2

Scaling plot of the surface particle density at $R=0.5$ and at $R=1.5$ (inset).

Figure 3

Numerical estimates of the exponents $x=\beta /{\nu }_{\perp }$ (circles) and $x_s$ (squares). The broken lines indicate the value at the strong disorder fixed point. The errors are of the same order as the size of the symbols.

Figure 4

Scaling of the gap to the first excited state at $R=1.5$ and $A=A_c=1.18$ [$L=16$ (+), 20 (□), 24 (○)].