diff --git a/examples/instances/3x3x2.txt b/examples/instances/3x3x2.txt
new file mode 100644
index 0000000..0e603cb
--- /dev/null
+++ b/examples/instances/3x3x2.txt
@@ -0,0 +1,89 @@
+1 2 -0.5320600854590267
+3 4 0.38402265869664154
+3 1 -0.5436924524983267
+3 2 0.21977738991479145
+4 1 -0.5628699912291399
+4 2 0.7923812769160723
+5 6 0.38332124497444475
+5 3 -0.2766447992621366
+5 4 0.43076811014522653
+6 3 0.08210571803994982
+6 4 -0.9915874978177643
+7 8 0.6014253456011047
+7 1 0.37763583164851355
+7 2 -0.26590744578208203
+8 1 0.9690946973530548
+8 2 -0.67694551766651
+9 10 -0.14153430905690412
+9 3 0.16759090162116919
+9 4 -0.8174998097136141
+10 3 -0.40403760194281046
+10 4 -0.6356483089131602
+9 7 0.04392506131183804
+9 8 0.9829874976922899
+10 7 -0.35689548049316144
+10 8 -0.1672648223095825
+9 1 -0.5786261566035802
+9 2 -0.34406623378116596
+10 1 0.100481750570526
+10 2 0.8038842162474464
+11 12 -0.8956911493893849
+11 5 -0.8630057217020062
+11 6 0.6306623988860585
+12 5 0.7504141436046725
+12 6 -0.9352371863606841
+11 9 -0.6803222587957678
+11 10 0.689782704271011
+12 9 0.7752150591589735
+12 10 -0.8343312141855883
+11 3 -0.5559557250718317
+11 4 0.17582966006044876
+12 3 0.19181763419530173
+12 4 0.27431075715253805
+13 14 0.7478095997218
+13 7 -0.4883614012946449
+13 8 0.9576256441396791
+14 7 -0.28912688765567185
+14 8 0.1089802463072973
+15 16 0.38262916472610375
+15 9 -0.3873909056772129
+15 10 -0.25725344989877863
+16 9 0.28309439316509377
+16 10 0.2501090573988438
+15 13 -0.6485175435412747
+15 14 -0.7668063443712008
+16 13 0.8137706230969115
+16 14 -0.2661847224606624
+15 7 -0.6442936476294694
+15 8 -0.5878720857895017
+16 7 -0.2581141133504936
+16 8 0.8888574164902534
+17 18 0.041339313482924744
+17 11 0.08787406849163526
+17 12 0.3277246664347784
+18 11 0.6635244080829124
+18 12 0.895970973800222
+17 15 -0.8035789245059162
+17 16 -0.21808521717755824
+18 15 -0.08569957531620931
+18 16 -0.49482281831259667
+17 9 0.2431182105351657
+17 10 0.20271622624323782
+18 9 0.6760555244443007
+18 10 -0.9602980312054934
+3 7 -0.24974831265384578
+3 8 0.9495698025338444
+4 7 0.8113253594825927
+4 8 0.7115673096585802
+5 9 0.025972963895515067
+5 10 -0.05189668641649137
+6 9 -0.28231537364653914
+6 10 -0.6298126342821251
+9 13 -0.17065967935812698
+9 14 -0.5828355422867022
+10 13 -0.6395271429265674
+10 14 -0.6326498113627528
+11 15 -0.342645305990952
+11 16 -0.6444311859249112
+12 15 0.5023530387484465
+12 16 0.4161687742404492
\ No newline at end of file
diff --git a/examples/ising_model_on_a_kings_graph.jl b/examples/ising_model_on_a_kings_graph.jl
new file mode 100644
index 0000000..3f07262
--- /dev/null
+++ b/examples/ising_model_on_a_kings_graph.jl
@@ -0,0 +1,57 @@
+using SpinGlassPEPS
+
+function get_instance(topology::NTuple{3, Int})
+    m, n, t = topology
+    "$(@__DIR__)/instances/$(m)x$(n)x$(t).txt"
+end
+
+function run_square_diag_bench(::Type{T}; topology::NTuple{3, Int}) where {T}
+    m, n, _ = topology
+    instance = get_instance(topology)
+    lattice = super_square_lattice(topology)
+
+    best_energies = T[]
+
+    potts_h = potts_hamiltonian(
+        ising_graph(instance),
+        spectrum = full_spectrum,
+        cluster_assignment_rule = lattice,
+    )
+
+    params = MpsParameters{T}(; bond_dim = 16, num_sweeps = 1)
+    search_params = SearchParameters(; max_states = 2^8, cutoff_prob = 1E-4)
+
+    for transform ∈ all_lattice_transformations
+        net = PEPSNetwork{KingSingleNode{GaugesEnergy}, Dense, T}(
+            m, n, potts_h, transform,
+        )
+
+        ctr = MpsContractor{SVDTruncate, NoUpdate, T}(
+            net, params; 
+            onGPU = false, beta = T(2), graduate_truncation = true,
+        )
+
+        # After update to SpinGlassEngine 1.5
+        # ctr = MpsContractor(SVDTruncate, net, params; 
+        # onGPU = false, beta = T(2), graduate_truncation = true,
+        # )
+
+        droplets = SingleLayerDroplets(; max_energy = 10, min_size = 5, metric = :hamming)
+        merge_strategy = merge_branches(
+            ctr; merge_prob = :none , droplets_encoding = droplets,
+        )
+
+        sol, info = low_energy_spectrum(ctr, search_params, merge_strategy)
+
+        push!(best_energies, sol.energies[1])
+        clear_memoize_cache()
+    end
+
+    ground = minimum(best_energies)
+    @assert all(ground .≈ best_energies)
+
+    println("Best energy found: $(ground)")
+end
+
+T = Float32
+@time run_square_diag_bench(T; topology = (3, 3, 2))
\ No newline at end of file