Table 7 Table of critical exponents for longer-range two orbital model with \(t=0.5\) obtained by an analysis of Eqs. (14) and (7).

From: Critical scaling of a two-orbital topological model with extended neighboring couplings

r

\(\hspace{0.13cm}\alpha \hspace{0.13cm}\)

\(\epsilon\)

\((|A_2|,|A_4|)\)

(|A|, |B|)

\(k_0=0\)

\(k_0=\pi\)

  

\((k_0=0,\pi )\)

\((k_0=0,\pi )\)

\((k_0=0,\pi )\)

\((z,\nu )\)

\((z,\nu )\)

2

0

(\(-\) 2,0)

(36,–)(4,–)

(600,–)(200,–)

(1,1)

(1,1)

0.1

(\(-\) 1.93,0.06)

(32.8573,–)(3.0003,–)

(944.963,–)(440.296,–)

(1,1)

(1,1)

0.5

(\(-\) 1.70,0.29)

(23.3137,–)(0.6863,–)

(1145.93,–)(143.167,–)

(1,1)

(1,1)

0.9

(\(-\) 1.53,0.46)

(17.1690,–)(0.0206,–)

(2336.42,–)(17.4493,–)

(1,1)

(1,1)

1

(\(-\) 1.5,0.5)

(16,–)(0,4.12)

(400,–)(0,3.81)

(1,1)

(2,1/2)

1.1

(\(-\) 1.46,0.53)

(14.9465,–)(0.0179,–)

(1274.67,–)(19.224,–)

(1,1)

(1,1)

1.4

(\(-\) 1.37,0.62)

(12.3603,–)(0.2345,–)

(447.39,–)(226.119,–)

(1,1)

(1,1)

1.9

(\(-\) 1.26,0.73)

(9.4358,–)(0.8616,–)

(521.813,–)(225.666,–)

(1,1)

(1,1)

3

0

(\(-\) 3,1)

(144,–)(16,–)

(1200,–)(400,–)

(1,1)

(1,1)

0.1

(\(-\) 2.82,0.96)

(123.3850,–)(13.2760,–)

(1391.46,–)(622.741,–)

(1,1)

(1,1)

0.5

(\(-\) 2.28,0.87)

(68.7660,–)(6.9468,–)

(930.271,–)(5412.33,–)

(1,1)

(1,1)

0.9

(\(-\) 1.90,0.8361)

(40.6507,–)(4.3627,–)

(1088.84,–)(904.726,–)

(1,1)

(1,1)

1

(\(-\) 1.83,0.8333)

(36,–)(4,–)

(489.273,–)(358.8,–)

(1,1)

(1,1)

1.1

(\(-\) 1.76,0.8321)

(32.0128,–)(3.7089,–)

(16708.4,–)(450.739,–)

(1,1)

(1,1)

1.4

(\(-\) 1.59,0.8358)

(23.0833,–)(3.1438,–)

(644.529,–)(1020.34,–)

(1,1)

(1,1)

1.9

(\(-\) 1.39,0.8561)

(14.5608,–)(2.7966,–)

(974.899,–)(781.219,–)

(1,1)

(1,1)

  1. Throughout the analysis, with the even number of neighbors, 1st TQCL \(k=0\) exhibits same universality class i.e., \((z=1, \nu =1)\). But 2nd TQCL \(k=\pi\) shows a breakdown at \(\alpha =1\) i.e., \((z=1, \nu =1)\) to \((z=2,\nu =1/2)\). For the odd interacting neighbors, the universality class remains same for both \(k=0\) and \(k=\pi\).