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peratures. As can be seem from this figure the estimate for the exponent ν , in the case Δ = 1 . 95, is closer to the expected tricritical value 40 / 77 = 0 . 519 · · · [48], than to the 2d Ising value ν = 1. 

## V. MULTICRITICAL POINTS AND THE STRONG DISORDER REGIME 

## A. A novel estimation of multicritical points 

From Fig. 4(a) one can observe the expected Ising loga- rithmic divergence of the specific heat maxima. Avoiding the value Δ = 1 . 95, which suffers from strong cross-over effects, we attempted to estimate the tricritical value of the crystal field by fitting the decreasing logarithmic am- plitudes C 2 to a suitable power law, as shown in Fig. 8. This may appear a naive or questionable idea, since the behavior of specific heat data is the Achilles’ heel of FSS analysis. Yet, Fig. 8 shows that besides the large fluctuations (errors) in logarithmic amplitudes C 2 , one could approximately estimate the tricritical crystal field 

<img src='content_image/427305.jpg'>

Δ$_{t}$ ≈ 1 . 96(1), as shown in the panel of Fig. 8. 

From Fig. 4(b) we observe again that, the specific heat maxima, corresponding now to the random-bond model at the disorder strength r = 0 . 75 / 1 . 25, are better- matched to the double-logarithmic divergence than the corresponding specific heat maxima of the pure model to a simple logarithmic divergence. Therefore, it appears realistic to try to obtain the multicritical point (more pre- cisely the value of the crystal field Δ$_{sd}$ where we expect the emergence of strong-disorder regime at a given dis- order strength), where the 2d random-bond (BC) Ising universality class meets the strong-disorder universality class, by fitting the decreasing double-logarithmic am- plitudes to a similar power law. Figure 9 presents now these fittings and also the estimated multicritical values of the crystal field Δ$_{sd}$ for the three disorder strengths considered in this paper. The statistical errors of the cor- responding double logarithmic amplitudes C 2 are seen to be quite smaller, compared to the corresponding ampli- tudes of the pure model, and the estimated values of the values of the multicritical field, shown in the panel of Fig. 9, appear more convincing. From their general trend we observe that as we increase the disorder strength the 

